Pub Date : 2023-01-09DOI: 10.1142/s0219265922500074
Hengzhe Li, Jiajia Wang, Rongxia Hao
Given a connected graph [Formula: see text] and [Formula: see text] with [Formula: see text], an [Formula: see text]-tree is a such subgraph [Formula: see text] of [Formula: see text] that is a tree with [Formula: see text]. Two [Formula: see text]-trees [Formula: see text] and [Formula: see text] are edge-disjoint if [Formula: see text]. Let [Formula: see text] be the maximum size of a set of edge-disjoint [Formula: see text]-trees in [Formula: see text]. The [Formula: see text]-connectivity of [Formula: see text] is defined as [Formula: see text]. In this paper, we first show some structural properties of edge-disjoint [Formula: see text]-trees by Fan Lemma and König-ore Formula. Then, the [Formula: see text]-connectivity of the Cartesian product of trees is determined. That is, let [Formula: see text] be trees, then [Formula: see text] if [Formula: see text] for each [Formula: see text], otherwise [Formula: see text]. As corollaries, [Formula: see text]-connectivity for some graph classes such as hypercubes and meshes can be obtained directly.
给定一个连通图[公式:见文]和[公式:见文]与[公式:见文]的连通图[公式:见文]，一个[公式:见文]树就是[公式:见文]的这样一个子图[公式:见文]，它是一个有[公式:见文]的树。如果[公式:见文本]，两个[公式:见文本]-树[公式:见文本]和[公式:见文本]是边不相交的。设[公式:见文]为[公式:见文]中一组边不相交的[公式:见文]树的最大大小。[公式:见文]的[公式:见文]-连通性被定义为[公式:见文]。在本文中，我们首先用范引理和König-ore公式证明了边不相交树的一些结构性质。然后，确定了树的笛卡尔积的连通性。也就是说，设[Formula: see text]为树，如果[Formula: see text]为每个[Formula: see text]，则[Formula: see text]为[Formula: see text]，否则为[Formula: see text]。作为推论，[公式:见文]-连通性的一些图类，如超立方体和网格可以直接得到。
{"title":"The λ4-Connectivity of the Cartesian Product of Trees","authors":"Hengzhe Li, Jiajia Wang, Rongxia Hao","doi":"10.1142/s0219265922500074","DOIUrl":"https://doi.org/10.1142/s0219265922500074","url":null,"abstract":"Given a connected graph [Formula: see text] and [Formula: see text] with [Formula: see text], an [Formula: see text]-tree is a such subgraph [Formula: see text] of [Formula: see text] that is a tree with [Formula: see text]. Two [Formula: see text]-trees [Formula: see text] and [Formula: see text] are edge-disjoint if [Formula: see text]. Let [Formula: see text] be the maximum size of a set of edge-disjoint [Formula: see text]-trees in [Formula: see text]. The [Formula: see text]-connectivity of [Formula: see text] is defined as [Formula: see text]. In this paper, we first show some structural properties of edge-disjoint [Formula: see text]-trees by Fan Lemma and König-ore Formula. Then, the [Formula: see text]-connectivity of the Cartesian product of trees is determined. That is, let [Formula: see text] be trees, then [Formula: see text] if [Formula: see text] for each [Formula: see text], otherwise [Formula: see text]. As corollaries, [Formula: see text]-connectivity for some graph classes such as hypercubes and meshes can be obtained directly.","PeriodicalId":153590,"journal":{"name":"J. Interconnect. Networks","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114131090","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 : 2022-12-28DOI: 10.1142/s0219265922500037
Gang Yang, Changxiang He
Let [Formula: see text] and [Formula: see text] be the vertex set and edge set of graph [Formula: see text]. Let [Formula: see text] be the distance between vertices [Formula: see text] and [Formula: see text] in the graph [Formula: see text] and [Formula: see text] be the graph obtained by deleting edge [Formula: see text] from [Formula: see text]. For a vertex set [Formula: see text] and an edge [Formula: see text], let [Formula: see text] be the set of pairs [Formula: see text] with a vertex [Formula: see text] and a vertex [Formula: see text] such that [Formula: see text]. A vertex set [Formula: see text] is distance-edge-monitoring set, introduced by Foucaud, Kao, Klasing, Miller, and Ryan, if every edge [Formula: see text] is monitored by some vertex of [Formula: see text], that is, the set [Formula: see text] is nonempty. In this paper, we determine the smallest size of distance-edge-monitoring sets of hierarchical and corona graphs.
设[公式:见文]和[公式:见文]分别为图[公式:见文]的顶点集和边集。设[公式:见文]为图[公式:见文]中顶点[公式:见文]与[公式:见文]之间的距离，[公式:见文]为从[公式:见文]中删除边[公式:见文]后得到的图。对于一个顶点集[公式:见文]和一条边[公式:见文]，设[公式:见文]是一个顶点[公式:见文]和一个顶点[公式:见文]的对[公式:见文]的集合，使得[公式:见文]。顶点集[Formula: see text]是由Foucaud、Kao、Klasing、Miller和Ryan引入的距离边监控集，如果每条边[Formula: see text]都被[Formula: see text]的某个顶点监控，即集合[Formula: see text]是非空的。在本文中，我们确定了分层图和电晕图的距离-边缘监测集的最小大小。
{"title":"Distance-Edge-Monitoring Sets in Hierarchical and Corona Graphs","authors":"Gang Yang, Changxiang He","doi":"10.1142/s0219265922500037","DOIUrl":"https://doi.org/10.1142/s0219265922500037","url":null,"abstract":"Let [Formula: see text] and [Formula: see text] be the vertex set and edge set of graph [Formula: see text]. Let [Formula: see text] be the distance between vertices [Formula: see text] and [Formula: see text] in the graph [Formula: see text] and [Formula: see text] be the graph obtained by deleting edge [Formula: see text] from [Formula: see text]. For a vertex set [Formula: see text] and an edge [Formula: see text], let [Formula: see text] be the set of pairs [Formula: see text] with a vertex [Formula: see text] and a vertex [Formula: see text] such that [Formula: see text]. A vertex set [Formula: see text] is distance-edge-monitoring set, introduced by Foucaud, Kao, Klasing, Miller, and Ryan, if every edge [Formula: see text] is monitored by some vertex of [Formula: see text], that is, the set [Formula: see text] is nonempty. In this paper, we determine the smallest size of distance-edge-monitoring sets of hierarchical and corona graphs.","PeriodicalId":153590,"journal":{"name":"J. Interconnect. Networks","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130459025","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 : 2022-12-24DOI: 10.1142/s0219265922500086
Junran Yu
Sun and Yeo introduced the concept of directed tree connectivity, including the generalized [Formula: see text]-vertex-strong connectivity, [Formula: see text] and generalized [Formula: see text]-arc-strong connectivity, [Formula: see text] [Formula: see text], which could be seen as a generalization of classical connectivity of digraphs and a natural extension of the well-established undirected tree connectivity. In this paper, we study the directed tree connectivity of symmetric digraphs and complete bipartite digraphs. We give lower bounds for the two parameters [Formula: see text] and [Formula: see text] on symmetric digraphs. We also determine the precise values of [Formula: see text] for every [Formula: see text] and [Formula: see text] for [Formula: see text], where [Formula: see text] is a complete bipartite digraph of order [Formula: see text].
{"title":"Directed Tree Connectivity of Symmetric Digraphs and Complete Bipartite Digraphs","authors":"Junran Yu","doi":"10.1142/s0219265922500086","DOIUrl":"https://doi.org/10.1142/s0219265922500086","url":null,"abstract":"Sun and Yeo introduced the concept of directed tree connectivity, including the generalized [Formula: see text]-vertex-strong connectivity, [Formula: see text] and generalized [Formula: see text]-arc-strong connectivity, [Formula: see text] [Formula: see text], which could be seen as a generalization of classical connectivity of digraphs and a natural extension of the well-established undirected tree connectivity. In this paper, we study the directed tree connectivity of symmetric digraphs and complete bipartite digraphs. We give lower bounds for the two parameters [Formula: see text] and [Formula: see text] on symmetric digraphs. We also determine the precise values of [Formula: see text] for every [Formula: see text] and [Formula: see text] for [Formula: see text], where [Formula: see text] is a complete bipartite digraph of order [Formula: see text].","PeriodicalId":153590,"journal":{"name":"J. Interconnect. Networks","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129058252","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 : 2022-12-19DOI: 10.1142/s0219265922500025
Maravarman Manoharan, S. Babu, R. Pitchai
Data security is critical in wireless sensor networks (WSNs) because communication signals are highly available due to data transmission in free space. Attacks ranging from passive eavesdropping to active snooping are more common on these networks. This paper proposes secure data transfer using data encryption based on the improved Rivest–Shamir–Adleman (RSA) with Diffie–Hellman (DH) key exchange algorithm (IRSA-DH). For this purpose, the adaptive distance-based agglomerative hierarchical (ADAH)-based clustering method is used. Then the cluster head (CH) is selected using the improved weight-based rain optimization (IWRO) to improve the network’s lifespan. This study aims to design a secure group communication method for WSNs. In order to generate and distribute the key to the group, the RSA and DH and key exchange algorithm had been hybridized with the Key Management Center (KMC). For safe communication between users, the key exchange technique is investigated. The performance measures such as throughput, packet loss ratio (PLR), packet delivery ratio (PDR), latency, energy consumption, end-to-end delay (EED) and network lifetime are analyzed and compared with the existing approaches.
{"title":"Wireless Sensor Network Security Analysis for Data and Aggregation","authors":"Maravarman Manoharan, S. Babu, R. Pitchai","doi":"10.1142/s0219265922500025","DOIUrl":"https://doi.org/10.1142/s0219265922500025","url":null,"abstract":"Data security is critical in wireless sensor networks (WSNs) because communication signals are highly available due to data transmission in free space. Attacks ranging from passive eavesdropping to active snooping are more common on these networks. This paper proposes secure data transfer using data encryption based on the improved Rivest–Shamir–Adleman (RSA) with Diffie–Hellman (DH) key exchange algorithm (IRSA-DH). For this purpose, the adaptive distance-based agglomerative hierarchical (ADAH)-based clustering method is used. Then the cluster head (CH) is selected using the improved weight-based rain optimization (IWRO) to improve the network’s lifespan. This study aims to design a secure group communication method for WSNs. In order to generate and distribute the key to the group, the RSA and DH and key exchange algorithm had been hybridized with the Key Management Center (KMC). For safe communication between users, the key exchange technique is investigated. The performance measures such as throughput, packet loss ratio (PLR), packet delivery ratio (PDR), latency, energy consumption, end-to-end delay (EED) and network lifetime are analyzed and compared with the existing approaches.","PeriodicalId":153590,"journal":{"name":"J. Interconnect. Networks","volume":"429 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116012989","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 : 2022-11-21DOI: 10.1142/s0219265922500013
Driss Ait Omar, Hamid Garmani, Mohamed EL Amrani, Es-said Azougaghe, Mohamed Baslam, M. Jourhmane
In this paper, to avoid congestion in the wireless channel of vehicular ad hoc networks (VANETs), a joint beaconing rate and beaconing power based on game theory are proposed in this paper. The game is formulated as a non-cooperative game, a Bayesian game, and a cooperative game. Three distributed and iterative algorithms (Best Response Algorithm, Fictitious Play Algorithm, and Cooperative Bargaining Algorithm) are proposed for computing the beaconing power and beaconing rate of each vehicle. Extensive simulations show the convergence of a proposed algorithm to the equilibrium beaconing power and beaconing rate and give some insights on how the game parameters may vary the game outcome.
{"title":"Towards Intelligent Control of Beaconing Power and Beaconing Rate in Vehicular Ad Hoc Networks","authors":"Driss Ait Omar, Hamid Garmani, Mohamed EL Amrani, Es-said Azougaghe, Mohamed Baslam, M. Jourhmane","doi":"10.1142/s0219265922500013","DOIUrl":"https://doi.org/10.1142/s0219265922500013","url":null,"abstract":"In this paper, to avoid congestion in the wireless channel of vehicular ad hoc networks (VANETs), a joint beaconing rate and beaconing power based on game theory are proposed in this paper. The game is formulated as a non-cooperative game, a Bayesian game, and a cooperative game. Three distributed and iterative algorithms (Best Response Algorithm, Fictitious Play Algorithm, and Cooperative Bargaining Algorithm) are proposed for computing the beaconing power and beaconing rate of each vehicle. Extensive simulations show the convergence of a proposed algorithm to the equilibrium beaconing power and beaconing rate and give some insights on how the game parameters may vary the game outcome.","PeriodicalId":153590,"journal":{"name":"J. Interconnect. Networks","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134017495","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 : 2022-10-29DOI: 10.1142/s0219265921500390
Mallanagouda Biradar, Basavaraj Mathapathi
One of the significant approaches in implementing the routing of WSNs is clustering that leads to scalability and extending of network lifetime. In the clustered WSN, cluster heads (CHs) utilize maximum energy to another node. Moreover, it balanced the load present in the sensor nodes (SNs) between the CHS for enhancing the network lifespan. Moreover, the CH plays an important part in efficient routing, as well as it must be selected in an optimal way. Thus, this work intends to introduce a cluster-based routing approach in WSN, where it selects the CHs by the optimization algorithm. A new hybrid seagull rock swarm with opposition-based learning (HSROBL) is introduced for this purpose, which is the hybridized concept of rock hyraxes swarm optimization (RHSO) and seagull optimization algorithm (SOA). Further, the optimal CH selection is based on various parameters including distance, security, delay, and energy. At the end, the outcomes of the presented approach are analyzed to extant algorithms based on delay, alive nodes, average throughput, and residual energy, respectively. Based on throughput, alive node, residual energy, as well as delay, the overall improvement in performance is about 28.50%.
{"title":"Security and Energy Aware Clustering-Based Routing in Wireless Sensor Network: Hybrid Nature-Inspired Algorithm for Optimal Cluster Head Selection","authors":"Mallanagouda Biradar, Basavaraj Mathapathi","doi":"10.1142/s0219265921500390","DOIUrl":"https://doi.org/10.1142/s0219265921500390","url":null,"abstract":"One of the significant approaches in implementing the routing of WSNs is clustering that leads to scalability and extending of network lifetime. In the clustered WSN, cluster heads (CHs) utilize maximum energy to another node. Moreover, it balanced the load present in the sensor nodes (SNs) between the CHS for enhancing the network lifespan. Moreover, the CH plays an important part in efficient routing, as well as it must be selected in an optimal way. Thus, this work intends to introduce a cluster-based routing approach in WSN, where it selects the CHs by the optimization algorithm. A new hybrid seagull rock swarm with opposition-based learning (HSROBL) is introduced for this purpose, which is the hybridized concept of rock hyraxes swarm optimization (RHSO) and seagull optimization algorithm (SOA). Further, the optimal CH selection is based on various parameters including distance, security, delay, and energy. At the end, the outcomes of the presented approach are analyzed to extant algorithms based on delay, alive nodes, average throughput, and residual energy, respectively. Based on throughput, alive node, residual energy, as well as delay, the overall improvement in performance is about 28.50%.","PeriodicalId":153590,"journal":{"name":"J. Interconnect. Networks","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125005655","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 : 2022-09-29DOI: 10.1142/s0219265921500407
Xueli Sun, Jianxi Fan, B. Cheng, Yan Wang, Jingya Zhou
Fault tolerance is critical to reliability analysis of interconnection networks since the vulnerability of component failure increases with the growth of network scale. Extra connectivity and extra diagnosability are two decisive indicators of the ability of parallel and distributed systems to tolerate and diagnose faulty nodes. This paper mainly establishes the [Formula: see text]-extra connectivity and [Formula: see text]-extra diagnosability of augmented [Formula: see text]-ary [Formula: see text]-cubes [Formula: see text], which is a generalization of [Formula: see text]-ary [Formula: see text]-cubes and augmented cubes. In addition, we explore the [Formula: see text]-extra diagnosis algorithm of [Formula: see text] under the MM* model.
随着网络规模的扩大，组件失效的脆弱性也随之增加，因此容错对互连网络的可靠性分析至关重要。额外的连通性和额外的可诊断性是并行和分布式系统容忍和诊断故障节点能力的两个决定性指标。本文主要建立了增广[公式:见文]-额外连通性[公式:见文]-ary[公式:见文]-立方体[公式:见文]的额外可诊断性[公式:见文]，这是对[公式:见文]-ary[公式:见文]-立方体和增广立方体的推广。此外，我们还探索了MM*模型下[Formula: see text]- [Formula: see text]的额外诊断算法。
{"title":"Reliability of Augmented 3-Ary n-Cubes with Extra Faults","authors":"Xueli Sun, Jianxi Fan, B. Cheng, Yan Wang, Jingya Zhou","doi":"10.1142/s0219265921500407","DOIUrl":"https://doi.org/10.1142/s0219265921500407","url":null,"abstract":"Fault tolerance is critical to reliability analysis of interconnection networks since the vulnerability of component failure increases with the growth of network scale. Extra connectivity and extra diagnosability are two decisive indicators of the ability of parallel and distributed systems to tolerate and diagnose faulty nodes. This paper mainly establishes the [Formula: see text]-extra connectivity and [Formula: see text]-extra diagnosability of augmented [Formula: see text]-ary [Formula: see text]-cubes [Formula: see text], which is a generalization of [Formula: see text]-ary [Formula: see text]-cubes and augmented cubes. In addition, we explore the [Formula: see text]-extra diagnosis algorithm of [Formula: see text] under the MM* model.","PeriodicalId":153590,"journal":{"name":"J. Interconnect. Networks","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132675655","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 : 2022-09-21DOI: 10.1142/s0219265921500389
Zhengqi Yu, Shuming Zhou, Hong Zhang, Xiaoqing Liu
Large-scale multiprocessor systems or multicomputer systems based on networking have been extensively used in the big data era and social network. Fault tolerance is becoming an essential attribute in multiprocessor systems with the increase of the system scale. For any distinct vertices [Formula: see text], the local connectivity of [Formula: see text] and [Formula: see text], denoted by [Formula: see text], is the maximum number of independent [Formula: see text]-paths in system graph [Formula: see text]. The local edge connectivity of [Formula: see text], [Formula: see text], [Formula: see text], is defined similarly. For any [Formula: see text], [Formula: see text], if [Formula: see text] (or [Formula: see text], then [Formula: see text] is [Formula: see text]-distance optimally (edge) connected, where [Formula: see text] is the diameter of [Formula: see text] and [Formula: see text] is the degree of [Formula: see text]. For any integers [Formula: see text] subject to [Formula: see text], if [Formula: see text] is [Formula: see text]-distance optimally (edge) connected, then we call [Formula: see text] is [Formula: see text]-distance local optimally (edge) connected. In this work, we show that [Formula: see text] ([Formula: see text] is [Formula: see text]-arrangement graph) is [Formula: see text]-distance local optimally edge connected for [Formula: see text] and [Formula: see text].
{"title":"Distance Optimally Edge Connectedness of Arrangement Graph Based on Subgraph Fault Pattern","authors":"Zhengqi Yu, Shuming Zhou, Hong Zhang, Xiaoqing Liu","doi":"10.1142/s0219265921500389","DOIUrl":"https://doi.org/10.1142/s0219265921500389","url":null,"abstract":"Large-scale multiprocessor systems or multicomputer systems based on networking have been extensively used in the big data era and social network. Fault tolerance is becoming an essential attribute in multiprocessor systems with the increase of the system scale. For any distinct vertices [Formula: see text], the local connectivity of [Formula: see text] and [Formula: see text], denoted by [Formula: see text], is the maximum number of independent [Formula: see text]-paths in system graph [Formula: see text]. The local edge connectivity of [Formula: see text], [Formula: see text], [Formula: see text], is defined similarly. For any [Formula: see text], [Formula: see text], if [Formula: see text] (or [Formula: see text], then [Formula: see text] is [Formula: see text]-distance optimally (edge) connected, where [Formula: see text] is the diameter of [Formula: see text] and [Formula: see text] is the degree of [Formula: see text]. For any integers [Formula: see text] subject to [Formula: see text], if [Formula: see text] is [Formula: see text]-distance optimally (edge) connected, then we call [Formula: see text] is [Formula: see text]-distance local optimally (edge) connected. In this work, we show that [Formula: see text] ([Formula: see text] is [Formula: see text]-arrangement graph) is [Formula: see text]-distance local optimally edge connected for [Formula: see text] and [Formula: see text].","PeriodicalId":153590,"journal":{"name":"J. Interconnect. Networks","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121292333","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 : 2022-08-27DOI: 10.1142/s0219265921500365
Yiling Dong
Let [Formula: see text] be a digraph of order [Formula: see text], [Formula: see text] a subset of [Formula: see text] of size [Formula: see text] and [Formula: see text]. A strong subgraph [Formula: see text] of [Formula: see text] is called an [Formula: see text]-strong subgraph if [Formula: see text]. A pair of [Formula: see text]-strong subgraphs [Formula: see text] and [Formula: see text] is said to be arc-disjoint if [Formula: see text]. Let [Formula: see text] be the maximum number of arc-disjoint [Formula: see text]-strong subgraphs in [Formula: see text]. Sun and Gutin defined the strong subgraph [Formula: see text]-arc-connectivity as [Formula: see text] The new parameter [Formula: see text] could be seen as a generalization of classical edge-connectivity of undirected graphs. In this paper, we get precise values for the strong subgraph 3-arc-connectivity of Cartesian products of some digraph classes. Also, we prove that there is no upper bound on [Formula: see text] depending on [Formula: see text] and [Formula: see text].
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Pub Date : 2022-08-05DOI: 10.1142/s0219265921500377
M. Gholami, Hovhannes A. Harutyunyan, Edward Maraachlian
Broadcasting is disseminating information in a network where a specific message must spread to all network vertices as quickly as possible. Finding the minimum broadcast time of a vertex in an arbitrary network is proven to be NP-complete. However, this problem is solvable for a few families of networks. In this paper, we present an optimal algorithm for finding the broadcast time of any vertex in a fully connected tree ([Formula: see text]) in [Formula: see text] time. An [Formula: see text] is formed by attaching arbitrary trees to vertices of a complete graph of size [Formula: see text] where [Formula: see text] is the total number of vertices in the graph.
{"title":"Optimal Broadcasting in Fully Connected Trees","authors":"M. Gholami, Hovhannes A. Harutyunyan, Edward Maraachlian","doi":"10.1142/s0219265921500377","DOIUrl":"https://doi.org/10.1142/s0219265921500377","url":null,"abstract":"Broadcasting is disseminating information in a network where a specific message must spread to all network vertices as quickly as possible. Finding the minimum broadcast time of a vertex in an arbitrary network is proven to be NP-complete. However, this problem is solvable for a few families of networks. In this paper, we present an optimal algorithm for finding the broadcast time of any vertex in a fully connected tree ([Formula: see text]) in [Formula: see text] time. An [Formula: see text] is formed by attaching arbitrary trees to vertices of a complete graph of size [Formula: see text] where [Formula: see text] is the total number of vertices in the graph.","PeriodicalId":153590,"journal":{"name":"J. Interconnect. Networks","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114633425","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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