Pub Date : 2023-04-03DOI: 10.1080/23799927.2023.2199304
Lantao You, J. Jiang, Yuejuan Han
ABSTRACT The communication performance and symmetry properties are two vital properties for a multiprocessor interconnection network. Diameter is an important factor to determine the communication performance of a graph. In a vertex-transitive graph, every vertex is identical to every other vertex in relation to its location. In this paper, we study the communication performance and vertex-transitivity property of the folded locally twisted cube . We find that the diameter of is , which is less than the diameter proposed by Peng [S. Peng, C. Guo, B. Yang, Topological properties of folded locally twisted cubes, Journal of Computational Information Systems, 11 (2015) 7667–7676]. And we prove that is vertex-transitive for n = 2, and is not vertex-transitive for .
{"title":"Communication performance and vertex-transitivity on folded locally twisted cube","authors":"Lantao You, J. Jiang, Yuejuan Han","doi":"10.1080/23799927.2023.2199304","DOIUrl":"https://doi.org/10.1080/23799927.2023.2199304","url":null,"abstract":"ABSTRACT The communication performance and symmetry properties are two vital properties for a multiprocessor interconnection network. Diameter is an important factor to determine the communication performance of a graph. In a vertex-transitive graph, every vertex is identical to every other vertex in relation to its location. In this paper, we study the communication performance and vertex-transitivity property of the folded locally twisted cube . We find that the diameter of is , which is less than the diameter proposed by Peng [S. Peng, C. Guo, B. Yang, Topological properties of folded locally twisted cubes, Journal of Computational Information Systems, 11 (2015) 7667–7676]. And we prove that is vertex-transitive for n = 2, and is not vertex-transitive for .","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83400005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-20DOI: 10.1080/23799927.2023.2193177
Mushtaq Taleb, Ruzelan Khalid, Mamdooh Attallah, Razamin Ramli, M. Nawawi
ABSTRACT Supply chain management (SCM) has been received much attention from academics and corporates. Effective and sustainable SCM require proper efficiency evaluation of suppliers. Such evaluation can be performed using data envelopment analysis (DEA). Classical DEA models presume all inputs and outputs are under the control of suppliers’ management, as well as the models cannot provide a complete ranking of efficient and inefficient suppliers. However, in SCM and other real-managerial problems, some inputs and/or outputs may be uncontrollable (outside management control). Thus, this paper proposes a super efficiency of slacks-based measure (SE-SBM) approach that can handle uncontrollable factors. The proposed approach can distinguish between efficient and inefficient suppliers and identify their rankings. The discriminating power of the proposed approach is due to it concurrently deals with input excesses and output shortfalls to improve inefficient suppliers, as well as input savings and output surpluses of efficient suppliers to maintain their efficient status.
{"title":"Evaluating efficiency and ranking of suppliers using non-radial super-efficiency data envelopment analysis with uncontrollable factors","authors":"Mushtaq Taleb, Ruzelan Khalid, Mamdooh Attallah, Razamin Ramli, M. Nawawi","doi":"10.1080/23799927.2023.2193177","DOIUrl":"https://doi.org/10.1080/23799927.2023.2193177","url":null,"abstract":"ABSTRACT Supply chain management (SCM) has been received much attention from academics and corporates. Effective and sustainable SCM require proper efficiency evaluation of suppliers. Such evaluation can be performed using data envelopment analysis (DEA). Classical DEA models presume all inputs and outputs are under the control of suppliers’ management, as well as the models cannot provide a complete ranking of efficient and inefficient suppliers. However, in SCM and other real-managerial problems, some inputs and/or outputs may be uncontrollable (outside management control). Thus, this paper proposes a super efficiency of slacks-based measure (SE-SBM) approach that can handle uncontrollable factors. The proposed approach can distinguish between efficient and inefficient suppliers and identify their rankings. The discriminating power of the proposed approach is due to it concurrently deals with input excesses and output shortfalls to improve inefficient suppliers, as well as input savings and output surpluses of efficient suppliers to maintain their efficient status.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83310878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-13DOI: 10.1080/23799927.2023.2190038
Yue Li, Fengyun Ren, Xinxin Xu, Qin Tong
For a set of connected subgraphs, an -factor denotes a spanning subgraph D of G if each component of D is isomorphic to a member of . In this paper, some sufficient conditions with regard to tight toughness, isolated toughness and binding number bounds to guarantee the existence of the -factor and -factor for a graph are obtained.
{"title":"Tight toughness, isolated toughness and binding number bounds for the path factors","authors":"Yue Li, Fengyun Ren, Xinxin Xu, Qin Tong","doi":"10.1080/23799927.2023.2190038","DOIUrl":"https://doi.org/10.1080/23799927.2023.2190038","url":null,"abstract":"For a set of connected subgraphs, an -factor denotes a spanning subgraph D of G if each component of D is isomorphic to a member of . In this paper, some sufficient conditions with regard to tight toughness, isolated toughness and binding number bounds to guarantee the existence of the -factor and -factor for a graph are obtained.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83877452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-23DOI: 10.1080/23799927.2023.2182234
S. Sharma, V. K. Bhat
ABSTRACT In this work, we introduce the concept of independence in multiresolving sets and present some basic results on it. We characterize two graph families for which we prove that their multiset dimension is three. We also provide a corrected proof for the multiset dimension of the grid graph , due to Simanjuntak et al., present in the literature.
{"title":"Independence in multiresolving sets of graphs","authors":"S. Sharma, V. K. Bhat","doi":"10.1080/23799927.2023.2182234","DOIUrl":"https://doi.org/10.1080/23799927.2023.2182234","url":null,"abstract":"ABSTRACT In this work, we introduce the concept of independence in multiresolving sets and present some basic results on it. We characterize two graph families for which we prove that their multiset dimension is three. We also provide a corrected proof for the multiset dimension of the grid graph , due to Simanjuntak et al., present in the literature.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82290614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-02DOI: 10.1080/23799927.2023.2184722
K. Ganesamoorthy, S. Priya
For a connected graph of order at least two, a connected outer connected monophonic set of is called a minimal connected outer connected monophonic set if no proper subset of is a connected outer connected monophonic set of . The upper connected outer connected monophonic number of is the maximum cardinality of a minimal connected outer connected monophonic set of . We determine bounds for it and find the upper connected outer connected monophonic number of certain classes of graphs. It is shown that for any two integers with , there is a connected graph of order with and . Also, for any three integers and with , there is a connected graph with and and a minimal connected outer connected monophonic set of cardinality , where is the connected outer connected monophonic number of a graph.
{"title":"The upper connected outer connected monophonic number of a graph","authors":"K. Ganesamoorthy, S. Priya","doi":"10.1080/23799927.2023.2184722","DOIUrl":"https://doi.org/10.1080/23799927.2023.2184722","url":null,"abstract":"For a connected graph of order at least two, a connected outer connected monophonic set of is called a minimal connected outer connected monophonic set if no proper subset of is a connected outer connected monophonic set of . The upper connected outer connected monophonic number of is the maximum cardinality of a minimal connected outer connected monophonic set of . We determine bounds for it and find the upper connected outer connected monophonic number of certain classes of graphs. It is shown that for any two integers with , there is a connected graph of order with and . Also, for any three integers and with , there is a connected graph with and and a minimal connected outer connected monophonic set of cardinality , where is the connected outer connected monophonic number of a graph.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88515294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-02DOI: 10.1080/23799927.2023.2184723
Yuya Higashikawa, N. Katoh, Yuki Kobayashi
We investigate the Euclidean minimum weight Laman graph on a planar point set P, for short. Bereg et al. (2016) studied geometric properties of and showed that the upper and lower bounds for the total number of edge crossings in are and , respectively. In this paper, we improve these upper and lower bounds to and for any , respectively. For improving the upper bound, we introduce a novel counting scheme based on some geometric observations. We also propose an time algorithm for computing , which was regarded as one of interesting future works by Bereg et al. (2016).
研究了平面点集P上的欧几里得最小权值拉曼图。Bereg et al.(2016)研究了的几何性质，并表明，边缘交叉总数的上限和下限分别为和。在本文中，我们分别改进了和的上界和下界。为了改进上界，我们引入了一种新的基于几何观察的计数方案。我们还提出了一种用于计算的时间算法，这被Bereg等人(2016)视为有趣的未来工作之一。
{"title":"Efficient algorithms and edge crossing properties of Euclidean minimum weight Laman graphs","authors":"Yuya Higashikawa, N. Katoh, Yuki Kobayashi","doi":"10.1080/23799927.2023.2184723","DOIUrl":"https://doi.org/10.1080/23799927.2023.2184723","url":null,"abstract":"We investigate the Euclidean minimum weight Laman graph on a planar point set P, for short. Bereg et al. (2016) studied geometric properties of and showed that the upper and lower bounds for the total number of edge crossings in are and , respectively. In this paper, we improve these upper and lower bounds to and for any , respectively. For improving the upper bound, we introduce a novel counting scheme based on some geometric observations. We also propose an time algorithm for computing , which was regarded as one of interesting future works by Bereg et al. (2016).","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82683208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-02DOI: 10.1080/23799927.2023.2185543
Y. Yanagisawa, Akira Suzuki, Yuma Tamura, Xiao Zhou
Suppose that we are given a positive integer k, and a k-(vertex-)colouring of a given graph G. Then we are asked to find a colouring of G using the minimum number of colours among colourings that are reachable from by iteratively changing a colour assignment of exactly one vertex while maintaining the property of k-colourings. In this paper, we give linear-time algorithms to solve the problem for graphs of degeneracy at most two and for the case where . These results imply linear-time algorithms for series-parallel graphs and grid graphs. In addition, we give linear-time algorithms for chordal graphs and cographs. On the other hand, we show that, for any , this problem remains NP-hard for planar graphs with degeneracy three and maximum degree four. Thus, we obtain a complexity dichotomy for this problem with respect to the degeneracy of a graph and the number k of colours.
{"title":"Decremental optimization of vertex-colouring under the reconfiguration framework","authors":"Y. Yanagisawa, Akira Suzuki, Yuma Tamura, Xiao Zhou","doi":"10.1080/23799927.2023.2185543","DOIUrl":"https://doi.org/10.1080/23799927.2023.2185543","url":null,"abstract":"Suppose that we are given a positive integer k, and a k-(vertex-)colouring of a given graph G. Then we are asked to find a colouring of G using the minimum number of colours among colourings that are reachable from by iteratively changing a colour assignment of exactly one vertex while maintaining the property of k-colourings. In this paper, we give linear-time algorithms to solve the problem for graphs of degeneracy at most two and for the case where . These results imply linear-time algorithms for series-parallel graphs and grid graphs. In addition, we give linear-time algorithms for chordal graphs and cographs. On the other hand, we show that, for any , this problem remains NP-hard for planar graphs with degeneracy three and maximum degree four. Thus, we obtain a complexity dichotomy for this problem with respect to the degeneracy of a graph and the number k of colours.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76029729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-12DOI: 10.1080/23799927.2022.2123405
Heqin Liu, Dongqin Cheng
ABSTRACT In recent years, a growing number of concepts have been proposed to better assess network fault tolerance, among which the generalized -connectivity has been widely used in the research of fault tolerance of interconnection networks. For connected graph , refers to the maximum number of internally disjoint trees in to connect , where with . The generalized -connectivity of G . The -dimensional folded hypercube , as a hypercube-like network, is obtained by adding edges on -dimensional hypercube . In this paper, we discuss the generalized 4-connectivity of and show that for .
{"title":"The generalized 4-connectivity of folded hypercube","authors":"Heqin Liu, Dongqin Cheng","doi":"10.1080/23799927.2022.2123405","DOIUrl":"https://doi.org/10.1080/23799927.2022.2123405","url":null,"abstract":"ABSTRACT In recent years, a growing number of concepts have been proposed to better assess network fault tolerance, among which the generalized -connectivity has been widely used in the research of fault tolerance of interconnection networks. For connected graph , refers to the maximum number of internally disjoint trees in to connect , where with . The generalized -connectivity of G . The -dimensional folded hypercube , as a hypercube-like network, is obtained by adding edges on -dimensional hypercube . In this paper, we discuss the generalized 4-connectivity of and show that for .","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88309365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-30DOI: 10.1080/23799927.2022.2118622
W. Myint, Ryuhei Uehara, G. Viglietta
ABSTRACT We investigate a new variation of a token reconfiguration problem on graphs using the cyclic shift operation. A coloured or labelled token is placed on each vertex of a given graph, and a ‘move’ consists in choosing a cycle in the graph and shifting tokens by one position along its edges. Given a target arrangement of tokens on the graph, our goal is to find a shortest sequence of moves that will re-arrange the tokens as in the target arrangement. The novelty of our model is that tokens are allowed to shift along any cycle in the graph, as opposed to a given subset of its cycles. We first discuss the problem on special graph classes: we give efficient algorithms for optimally solving the 2-Coloured Token Shifting Problem on complete graphs and block graphs, as well as the Labelled Token Shifting Problem on complete graphs and variants of barbell graphs. We then show that, in the 2-Coloured Token Shifting Problem, the shortest sequence of moves is NP-hard to approximate within a factor of , even for grid graphs. The latter result settles an open problem posed by Sai et al.
{"title":"Token shifting on graphs","authors":"W. Myint, Ryuhei Uehara, G. Viglietta","doi":"10.1080/23799927.2022.2118622","DOIUrl":"https://doi.org/10.1080/23799927.2022.2118622","url":null,"abstract":"ABSTRACT We investigate a new variation of a token reconfiguration problem on graphs using the cyclic shift operation. A coloured or labelled token is placed on each vertex of a given graph, and a ‘move’ consists in choosing a cycle in the graph and shifting tokens by one position along its edges. Given a target arrangement of tokens on the graph, our goal is to find a shortest sequence of moves that will re-arrange the tokens as in the target arrangement. The novelty of our model is that tokens are allowed to shift along any cycle in the graph, as opposed to a given subset of its cycles. We first discuss the problem on special graph classes: we give efficient algorithms for optimally solving the 2-Coloured Token Shifting Problem on complete graphs and block graphs, as well as the Labelled Token Shifting Problem on complete graphs and variants of barbell graphs. We then show that, in the 2-Coloured Token Shifting Problem, the shortest sequence of moves is NP-hard to approximate within a factor of , even for grid graphs. The latter result settles an open problem posed by Sai et al.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72379079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-09DOI: 10.1080/23799927.2022.2110159
Sambhav Gupta, Eddie Cheng, László Lipták
ABSTRACT The conditional fractional strong matching preclusion number of a graph G is the minimum size of F such that and G−F has neither a fractional perfect matching nor an isolated vertex. In this paper, we obtain the conditional fractional strong matching preclusion number for burnt pancake graphs and a subset of the class of pancake-like graphs.
{"title":"Conditional fractional matching preclusion for burnt pancake graphs and pancake-like graphs","authors":"Sambhav Gupta, Eddie Cheng, László Lipták","doi":"10.1080/23799927.2022.2110159","DOIUrl":"https://doi.org/10.1080/23799927.2022.2110159","url":null,"abstract":"ABSTRACT The conditional fractional strong matching preclusion number of a graph G is the minimum size of F such that and G−F has neither a fractional perfect matching nor an isolated vertex. In this paper, we obtain the conditional fractional strong matching preclusion number for burnt pancake graphs and a subset of the class of pancake-like graphs.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78012151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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