Lantao You, Yuejuan Han, Xi Wang, Chen Zhou, Rui Gu, Chen Lu
{"title":"Structure Connectivity and Substructure Connectivity of Alternating Group Graphs","authors":"Lantao You, Yuejuan Han, Xi Wang, Chen Zhou, Rui Gu, Chen Lu","doi":"10.1109/PIC.2018.8706296","DOIUrl":null,"url":null,"abstract":"The alternating group graph, denoted by AGn, is one of the popular interconnection networks. In this paper, we consider two network connectivities, H-structure-connectivity and H-substructure-connectivity, which are new measures for a network’s reliability and fault-tolerability. We say that a set F of connected subgraphs of G is a subgraph-cut of G if G−V (F) is a disconnected or trivial graph. Let H be a connected subgraph of G. Then F is an H-structure-cut, if F is a subgraph-cut, and every element in F is isomorphic to H. And F is an H-substructure-cut if F is a subgraph-cut, such that every element in F is isomorphic to a connected subgraph of H. The H-structure-connectivity(resp. H-substructure-connectivity) of G, denoted by κ(G;H)(resp. κs(G;H)), is the minimum cardinality of all H-structure-cuts(resp. H-substructure-cuts) of G. In this paper, we will establish both κ(AGn;H) and κ(AGn;H) for the alternating group graph AGn and H ∈{K1,K1,1,K1,2}.","PeriodicalId":236106,"journal":{"name":"2018 IEEE International Conference on Progress in Informatics and Computing (PIC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 IEEE International Conference on Progress in Informatics and Computing (PIC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/PIC.2018.8706296","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
The alternating group graph, denoted by AGn, is one of the popular interconnection networks. In this paper, we consider two network connectivities, H-structure-connectivity and H-substructure-connectivity, which are new measures for a network’s reliability and fault-tolerability. We say that a set F of connected subgraphs of G is a subgraph-cut of G if G−V (F) is a disconnected or trivial graph. Let H be a connected subgraph of G. Then F is an H-structure-cut, if F is a subgraph-cut, and every element in F is isomorphic to H. And F is an H-substructure-cut if F is a subgraph-cut, such that every element in F is isomorphic to a connected subgraph of H. The H-structure-connectivity(resp. H-substructure-connectivity) of G, denoted by κ(G;H)(resp. κs(G;H)), is the minimum cardinality of all H-structure-cuts(resp. H-substructure-cuts) of G. In this paper, we will establish both κ(AGn;H) and κ(AGn;H) for the alternating group graph AGn and H ∈{K1,K1,1,K1,2}.