The information aggregation operator plays a key rule in the multiple attribute group decision making problems. The aim of this paper is to investigate the information aggregation operators method under the interval-valued picture fuzzy environment with the help of Frank norms operations. The picture fuzzy set is an extended version of the intuitionistic fuzzy set, which not only considers the degree of acceptance or rejection but also takes into the account of neutral degree during the analysis. Under these environments, some basic aggregation operators namely interval-valued picture fuzzy Frank weighted averaging operator, interval-valued picture fuzzy Frank ordered weighted averaging operator, interval-valued picture fuzzy Frank hybrid averaging operator, interval-valued picture fuzzy Frank weighted geometric operator, interval-valued picture fuzzy Frank ordered weighted geometric operator, and interval-valued picture fuzzy Frank hybrid geometric operator are proposed in this paper. Some general properties of these operators such as idempotency, commutativity, monotonicity, and boundedness, are discussed. Furthermore, the method for multiple attribute group decision making problems based on these operators is developed and the operational processes are illustrated in detail. Finally, an illustrative example has been given to show the decision steps of the proposed method and to demonstrate their effectiveness.
{"title":"Interval-valued picture fuzzy aggregation information based on Frank operators and their application in group decision making","authors":"Mohammad Ali Abolfathi, Ali Ebadian","doi":"10.1051/ro/2023174","DOIUrl":"https://doi.org/10.1051/ro/2023174","url":null,"abstract":"The information aggregation operator plays a key rule in the multiple attribute group decision making problems. The aim of this paper is to investigate the information aggregation operators method under the interval-valued picture fuzzy environment with the help of Frank norms operations. The picture fuzzy set is an extended version of the intuitionistic fuzzy set, which not only considers the degree of acceptance or rejection but also takes into the account of neutral degree during the analysis. Under these environments, some basic aggregation operators namely interval-valued picture fuzzy Frank weighted averaging operator, interval-valued picture fuzzy Frank ordered weighted averaging operator, interval-valued picture fuzzy Frank hybrid averaging operator, interval-valued picture fuzzy Frank weighted geometric operator, interval-valued picture fuzzy Frank ordered weighted geometric operator, and interval-valued picture fuzzy Frank hybrid geometric operator are proposed in this paper. Some general properties of these operators such as idempotency, commutativity, monotonicity, and boundedness, are discussed. Furthermore, the method for multiple attribute group decision making problems based on these operators is developed and the operational processes are illustrated in detail. Finally, an illustrative example has been given to show the decision steps of the proposed method and to demonstrate their effectiveness.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135475983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Sundara Rajan, Arulanand S, S. Prabhu, Indra Rajasingh
In a graph G, if each node v∈V (G)S is connected to some node in S, then the set S of nodes is referred to as a dominating set. The domination number of G is the minimum cardinality of all dominating sets of G and is represented by γ(G). If a dominating set S monitors every node in the system under a set of guidelines for power systems monitoring, then the set S is referred to as a power-dominating set of G. The power domination number of G is the least number of vertices of a power dominating set of G. A generalization of power domination is the k-power domination in a graph G. The k-power domination number of G is the minimum cardinality of all k-power dominating sets of G and is represented by γp,k(G). In this paper, we have obtained the 2-power domination number represented by γp,2(G) for 4-regular Kn¨odel graphs and given the lower bound for 5-regular Kn¨odel graphs.
在图G中，如果每个节点v∈v (G)S与S中的某个节点相连，则将节点的集合S称为支配集。G的支配数是G的所有支配集的最小基数，用γ(G)表示。如果支配集S监控系统下一组中的每个节点电力系统监测指南,然后集合S称为power-dominating组G G的权力支配数量最少的顶点的权力支配组G .泛化的权力统治是k次方统治图G·k次方统治的G的最低基数是所有k次方G和支配集是由γp k (G)。本文给出了4正则Kn型图的2次方支配数γp,2(G)，并给出了5正则Kn型图的下界。
{"title":"2-power domination number for Knodel graphs and its application in communication networks","authors":"R. Sundara Rajan, Arulanand S, S. Prabhu, Indra Rajasingh","doi":"10.1051/ro/2023173","DOIUrl":"https://doi.org/10.1051/ro/2023173","url":null,"abstract":"In a graph G, if each node v∈V (G)S is connected to some node in S, then the set S of nodes is referred to as a dominating set. The domination number of G is the minimum cardinality of all dominating sets of G and is represented by γ(G). If a dominating set S monitors every node in the system under a set of guidelines for power systems monitoring, then the set S is referred to as a power-dominating set of G. The power domination number of G is the least number of vertices of a power dominating set of G. A generalization of power domination is the k-power domination in a graph G. The k-power domination number of G is the minimum cardinality of all k-power dominating sets of G and is represented by γp,k(G). In this paper, we have obtained the 2-power domination number represented by γp,2(G) for 4-regular Kn¨odel graphs and given the lower bound for 5-regular Kn¨odel graphs.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"34 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Demographic changes, urbanization and increasing vehicle ownership at unprecedented rates put a lot of strain on cities particularly on urban mobility and transportation and overwhelm transportation network infrastructures and current transportation systems, which are not built to cope with such a fast increasing demand. Traffic congestion is considered as the most difficult challenge to tackle for sustainable urban mobility and is aggravated by the increased freight activity due to e-commerce and on-demand delivery and the explosive growth in transportation network companies and ride-hailing services. There is a need to implement a combination of policies to ensure that increased urban traffic congestion does not lower the quality of life and threaten global climate and human health and to prevent further economic losses. This study aims to contribute to the United Nations (UN) climate action and sustainable development goals in tackling recurring traffic congestion problem in urban areas to achieve a sustainable urban mobility in that it offers a solution methodology for traffic assignment problem. We introduce an exact generalized solution methodology based on reformulation of existing traffic assignment problems as a second order cone programming (SOCP) problem and propose column generation (CG) and cutting plane (CP) algorithms to solve the problem effectively for large scale road network instances. We conduct numerical experiments to test the performance of the proposed algorithms on realistic road networks.
{"title":"An exact second order cone programming approach for traffic assignment problems","authors":"Vedat Bayram","doi":"10.1051/ro/2023172","DOIUrl":"https://doi.org/10.1051/ro/2023172","url":null,"abstract":"Demographic changes, urbanization and increasing vehicle ownership at unprecedented rates put a lot of strain on cities particularly on urban mobility and transportation and overwhelm transportation network infrastructures and current transportation systems, which are not built to cope with such a fast increasing demand. Traffic congestion is considered as the most difficult challenge to tackle for sustainable urban mobility and is aggravated by the increased freight activity due to e-commerce and on-demand delivery and the explosive growth in transportation network companies and ride-hailing services. There is a need to implement a combination of policies to ensure that increased urban traffic congestion does not lower the quality of life and threaten global climate and human health and to prevent further economic losses. This study aims to contribute to the United Nations (UN) climate action and sustainable development goals in tackling recurring traffic congestion problem in urban areas to achieve a sustainable urban mobility in that it offers a solution methodology for traffic assignment problem. We introduce an exact generalized solution methodology based on reformulation of existing traffic assignment problems as a second order cone programming (SOCP) problem and propose column generation (CG) and cutting plane (CP) algorithms to solve the problem effectively for large scale road network instances. We conduct numerical experiments to test the performance of the proposed algorithms on realistic road networks.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"7 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134910013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
High online operating costs and low consumer utility still need to be addressed in the sales of community fresh e-commerce. Herein, we develop a new community fresh marketing model composed of retailers for online operating costs and consumers for low consumer utility by dividing community consumers into essential type and expectant type in this study. Then, the profit functions of community fresh retailers are developed in this study according to utility theory. Finally, a revised model of the fresh quality transparency (FQT) factor is conducted and discussed in this study. The results suggest that the profits obtained from essential consumers and expectant consumers by the community fresh e-commerce retailers are higher within a certain range of freshness costs compared to the basic model’s projection; meanwhile, the profits from expectant consumers contribute more than those from essential consumers. However, if the freshness cost exceeds a certain critical value, the abovementioned profits predicted from the new model will be lower. This study enriches the supply chain theory of community fresh food and provides retailers with theoretical guidance on differentiated services and pricing to better match the needs of community consumers.
{"title":"Price strategy of community fresh food e-commerce considering the heterogeneous needs of consumers and fresh quality transparency ","authors":"BING JIANG, HONGBING LUO, CHONG WANG, JIANKANG LIU, XIAOLING LIU, CHENG LIU, ZHENYI JI, DONG XIA","doi":"10.1051/ro/2023169","DOIUrl":"https://doi.org/10.1051/ro/2023169","url":null,"abstract":"High online operating costs and low consumer utility still need to be addressed in the sales of community fresh e-commerce. Herein, we develop a new community fresh marketing model composed of retailers for online operating costs and consumers for low consumer utility by dividing community consumers into essential type and expectant type in this study. Then, the profit functions of community fresh retailers are developed in this study according to utility theory. Finally, a revised model of the fresh quality transparency (FQT) factor is conducted and discussed in this study. The results suggest that the profits obtained from essential consumers and expectant consumers by the community fresh e-commerce retailers are higher within a certain range of freshness costs compared to the basic model’s projection; meanwhile, the profits from expectant consumers contribute more than those from essential consumers. However, if the freshness cost exceeds a certain critical value, the abovementioned profits predicted from the new model will be lower. This study enriches the supply chain theory of community fresh food and provides retailers with theoretical guidance on differentiated services and pricing to better match the needs of community consumers.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135217897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers a population model (system) which is prone to catastrophe that kills individuals in batches. Individuals enter the system in accordance with the renewal process and catastrophe occurs as per the Poisson process. The catastrophe attacks the population in a successive order in batches of random size, each batch of individuals dies with probability ξ. This successive process ends when the whole population is wiped out or a batch of individuals survives with probability 1 −ξ. This type of killing pattern is known as geometric catastrophe. The supplementary variable technique is used to develop the steady-state governing equations. Further using the difference operator, the distributions of population size are evaluated at arbitrary, pre-arrival, and post-catastrophe epochs. In addition to that, a few different measurements of the system’s performance are derived. In order to demonstrate the applicability of the model, a number of numerical and graphical outcomes are presented in the form of tables and graphs.
{"title":"Analysis of a renewal arrival process subject to geometric catastrophe with random batch killing","authors":"Nitin Kumar","doi":"10.1051/ro/2023171","DOIUrl":"https://doi.org/10.1051/ro/2023171","url":null,"abstract":"This paper considers a population model (system) which is prone to catastrophe that kills individuals in batches. Individuals enter the system in accordance with the renewal process and catastrophe occurs as per the Poisson process. The catastrophe attacks the population in a successive order in batches of random size, each batch of individuals dies with probability ξ. This successive process ends when the whole population is wiped out or a batch of individuals survives with probability 1 −ξ. This type of killing pattern is known as geometric catastrophe. The supplementary variable technique is used to develop the steady-state governing equations. Further using the difference operator, the distributions of population size are evaluated at arbitrary, pre-arrival, and post-catastrophe epochs. In addition to that, a few different measurements of the system’s performance are derived. In order to demonstrate the applicability of the model, a number of numerical and graphical outcomes are presented in the form of tables and graphs.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"4 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134974020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we deal with a portfolio optimization problem including both risky and risk-free assets. We use the infinity norm criterion to measure portfolio risk and formulate the problem as a bi-objective linear optimization problem. Then, a single objective linear program is considered related to the bi-objective optimization problem. Using the well-known Karush-Kuhn-Tucker optimality conditions, we obtain analytic formula for an optimal solution. Moreover, we determine the whole efficient frontier by multi-criteria optimization techniques. Based on the theoretical results, two algorithms are proposed for finding the portfolio weights and the efficient frontier. Numerical examples are given for illustrating the new models and algorithms. Additionally, a simulation study has been conducted to assess the performance of the proposed method.
{"title":"Portfolio optimization based on bi-objective linear programming","authors":"Marzie Izadi, Mohammad Ali Yaghoobi","doi":"10.1051/ro/2023170","DOIUrl":"https://doi.org/10.1051/ro/2023170","url":null,"abstract":"In this study, we deal with a portfolio optimization problem including both risky and risk-free assets. We use the infinity norm criterion to measure portfolio risk and formulate the problem as a bi-objective linear optimization problem. Then, a single objective linear program is considered related to the bi-objective optimization problem. Using the well-known Karush-Kuhn-Tucker optimality conditions, we obtain analytic formula for an optimal solution. Moreover, we determine the whole efficient frontier by multi-criteria optimization techniques. Based on the theoretical results, two algorithms are proposed for finding the portfolio weights and the efficient frontier. Numerical examples are given for illustrating the new models and algorithms. Additionally, a simulation study has been conducted to assess the performance of the proposed method.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"26 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134973501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The eccentricity matrix of a graph is defined as the matrix obtained from its distance matrix by retaining the largest elements in each row and column, while the rest elements are set to be zero. The eccentricity eigenvalues of a graph are the eigenvalues of its eccentricity matrix, the eccentricity energy of a graph is the sum of the absolute values of its eccentricity eigenvalues, and the eccentricity spectral radius of a graph is its largest eccentricity eigenvalue. Let Gn,d be the set of n-vertex connected graphs with odd diameter d, where each graph G in Gn,d has a diametrical path whose center edge is a cut edge of G. For any graph G in Gn,d, we construct a weighted graph Hω such that its adjacency matrix is just the eccentricity matrix of G, where H is the sequential join graph of the complement graphs of four disjoint complete graphs. In terms of the energy and spectral radius of the weighted graphs, we determine the graphs with minimum eccentricity energy, minimum and maximum eccentricity spectral radius, respectively, in Gn,d. As corollaries, we determine the trees with minimum eccentricity energy, minimum and maximum eccentricity spectral radius, respectively, among all trees with odd diameter.
{"title":"On the eccentricity energy and eccentricity spectral radius of graphs with odd diameter","authors":"Leshi Qiu, Jianping Li, Jianbin Zhang","doi":"10.1051/ro/2023168","DOIUrl":"https://doi.org/10.1051/ro/2023168","url":null,"abstract":"The eccentricity matrix of a graph is defined as the matrix obtained from its distance matrix by retaining the largest elements in each row and column, while the rest elements are set to be zero. The eccentricity eigenvalues of a graph are the eigenvalues of its eccentricity matrix, the eccentricity energy of a graph is the sum of the absolute values of its eccentricity eigenvalues, and the eccentricity spectral radius of a graph is its largest eccentricity eigenvalue. Let Gn,d be the set of n-vertex connected graphs with odd diameter d, where each graph G in Gn,d has a diametrical path whose center edge is a cut edge of G. For any graph G in Gn,d, we construct a weighted graph Hω such that its adjacency matrix is just the eccentricity matrix of G, where H is the sequential join graph of the complement graphs of four disjoint complete graphs. In terms of the energy and spectral radius of the weighted graphs, we determine the graphs with minimum eccentricity energy, minimum and maximum eccentricity spectral radius, respectively, in Gn,d. As corollaries, we determine the trees with minimum eccentricity energy, minimum and maximum eccentricity spectral radius, respectively, among all trees with odd diameter.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"37 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The dynamic mean-variance portfolio selection problem is time inconsistent. In the literature, scholars try to derive the precommitted strategy, the time consistent strategy and the self-coordination strategy. The pre-committed strategy only concern the global investment interest of the investor. The time consistent strategy only concerns the local investment interests of the investor, while the selfcoordination strategy balances between the global investment interest and local investment interests of the investor. However, the selfcoordination strategy is only studied for the discrete time mean-variance setting. We study the self-coordination strategy for the continuous time mean-variance setting in this paper. With the help of mean-field reformulation, we derive the analytical self-coordination mean-variance strategy and show that the pre-committed strategy and time consistent strategy are special cases of the self-coordination strategy.
{"title":"The self-coordination mean-variance strategy in continuous time","authors":"Yun Shi, Duan Li, Xiangyu Cui","doi":"10.1051/ro/2023166","DOIUrl":"https://doi.org/10.1051/ro/2023166","url":null,"abstract":"The dynamic mean-variance portfolio selection problem is time inconsistent. In the literature, scholars try to derive the precommitted strategy, the time consistent strategy and the self-coordination strategy. The pre-committed strategy only concern the global investment interest of the investor. The time consistent strategy only concerns the local investment interests of the investor, while the selfcoordination strategy balances between the global investment interest and local investment interests of the investor. However, the selfcoordination strategy is only studied for the discrete time mean-variance setting. We study the self-coordination strategy for the continuous time mean-variance setting in this paper. With the help of mean-field reformulation, we derive the analytical self-coordination mean-variance strategy and show that the pre-committed strategy and time consistent strategy are special cases of the self-coordination strategy.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135805233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the problem of data routing in backhaul networks using Unmanned Aerial Vehicles (UAVs) to relay data from Small Cells (SCs) to the core network. The objective is to maximize the total demand of data to be routed, while ensuring technical requirements such as hop constraints and edge capacity. The problem is formulated using a compact mixed-integer programming model, which can solve small- and medium-sized topologies. In addition, a fast constructive heuristic based on a maximal tree is developed to solve large-scale topologies, resulting in a significant reduction in CPU time. The quality of the heuristic is evaluated by using column generation for solving the linear programming relaxation of an exponential formulation. The computational study shows the effectiveness and value of the proposed compact model and constructive heuristic for various topology sizes. Furthermore, experiments demonstrates that by keeping the network setup constant and updating the demand vector only, the computational time of the compact model can be drastically reduced for all topology sizes.
{"title":"Exact and heuristic approaches for maximizing flows in UAV-enabled wireless cellular networks with multi-hop backhauls","authors":"Mohamed Haouari, Mariem Mhiri, Kais Msakni, Mazen Hasna, Tamer Khattab","doi":"10.1051/ro/2023167","DOIUrl":"https://doi.org/10.1051/ro/2023167","url":null,"abstract":"This paper investigates the problem of data routing in backhaul networks using Unmanned Aerial Vehicles (UAVs) to relay data from Small Cells (SCs) to the core network. The objective is to maximize the total demand of data to be routed, while ensuring technical requirements such as hop constraints and edge capacity. The problem is formulated using a compact mixed-integer programming model, which can solve small- and medium-sized topologies. In addition, a fast constructive heuristic based on a maximal tree is developed to solve large-scale topologies, resulting in a significant reduction in CPU time. The quality of the heuristic is evaluated by using column generation for solving the linear programming relaxation of an exponential formulation. The computational study shows the effectiveness and value of the proposed compact model and constructive heuristic for various topology sizes. Furthermore, experiments demonstrates that by keeping the network setup constant and updating the demand vector only, the computational time of the compact model can be drastically reduced for all topology sizes.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135855219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Deise L. de Oliveira, Danilo Artigas, Simone Dantas, Luisa Frickes, Atílio G. Luiz
A graceful labeling of a graph $G$ with $m$ edges consists in labeling the vertices of $G$ with distinct integers from $0$ to $m$ such that each edge is uniquely identified by the absolute difference of the labels of its endpoints. In this work, we study the graceful labeling problem in the context of maker-breaker graph games. The Graceful Game was introduced by Tuza, in 2017, as a two-players game on a connected graph in which the players, Alice and Bob, take moves labeling the vertices with distinct integers from $0$ to $m$. Players are constrained to use only legal labelings (moves), that is, after a move, all edge labels are distinct. Alice's goal is to obtain a graceful labeling for the graph, as Bob's goal is to prevent it from happening. In this work, we study winning strategies for Alice and Bob in graph classes: paths, complete graphs, cycles, complete bipartite graphs, caterpillars, trees, gear graphs, web graphs, prisms, hypercubes, 2-powers of paths, wheels and fan graphs.
{"title":"Graceful game on some graph classes","authors":"Deise L. de Oliveira, Danilo Artigas, Simone Dantas, Luisa Frickes, Atílio G. Luiz","doi":"10.1051/ro/2023165","DOIUrl":"https://doi.org/10.1051/ro/2023165","url":null,"abstract":"A graceful labeling of a graph $G$ with $m$ edges consists in labeling the vertices of $G$ with distinct integers from $0$ to $m$ such that each edge is uniquely identified by the absolute difference of the labels of its endpoints. In this work, we study the graceful labeling problem in the context of maker-breaker graph games. The Graceful Game was introduced by Tuza, in 2017, as a two-players game on a connected graph in which the players, Alice and Bob, take moves labeling the vertices with distinct integers from $0$ to $m$. Players are constrained to use only legal labelings (moves), that is, after a move, all edge labels are distinct. Alice's goal is to obtain a graceful labeling for the graph, as Bob's goal is to prevent it from happening. In this work, we study winning strategies for Alice and Bob in graph classes: paths, complete graphs, cycles, complete bipartite graphs, caterpillars, trees, gear graphs, web graphs, prisms, hypercubes, 2-powers of paths, wheels and fan graphs.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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