{"title":"The Generalized 3-Connectivity and 4-Connectivity of Crossed Cube","authors":"Heqin Liu, Dongqin Cheng","doi":"10.7151/dmgt.2474","DOIUrl":null,"url":null,"abstract":"Abstract The generalized connectivity, an extension of connectivity, provides a new reference for measuring the fault tolerance of networks. For any connected graph G, let S ⊆ V (G) and 2 ≤ |S| ≤ V (G); κG(S) refers to the maximum number of internally disjoint trees in G connecting S. The generalized k-connectivity of G, κk(G), is defined as the minimum value of κG(S) over all S ⊆ V (G) with |S| = k. The n-dimensional crossed cube CQn, as a hypercube-like network, is considered as an attractive alternative to hypercube network because of its many good properties. In this paper, we study the generalized 3-connectivity and the generalized 4-connectivity of CQnand obtain κ3(CQn) = κ4(CQn) = n − 1, where n ≥ 2.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discussiones Mathematicae Graph Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7151/dmgt.2474","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract The generalized connectivity, an extension of connectivity, provides a new reference for measuring the fault tolerance of networks. For any connected graph G, let S ⊆ V (G) and 2 ≤ |S| ≤ V (G); κG(S) refers to the maximum number of internally disjoint trees in G connecting S. The generalized k-connectivity of G, κk(G), is defined as the minimum value of κG(S) over all S ⊆ V (G) with |S| = k. The n-dimensional crossed cube CQn, as a hypercube-like network, is considered as an attractive alternative to hypercube network because of its many good properties. In this paper, we study the generalized 3-connectivity and the generalized 4-connectivity of CQnand obtain κ3(CQn) = κ4(CQn) = n − 1, where n ≥ 2.
期刊介绍:
The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.