图的分支点连通度和分支边连通度综述  

Component Connectivity and Component Edge Connectivity of Graphs:A Survey

作　　者：刘雪梅 孟吉翔[1] LIU Xuemei;MENG Jixiang(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《新疆大学学报（自然科学版）（中英文）》2023年第3期257-266,273,共11页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：supported by National Natural Science Foundation of Xingjiang,China“Fault-tolerance of graphs and networks”(2020D04046);National Natural Science Foundation of the People’s Republic of China“On the sizes of vertex(edge)-k-maximal r-uniform hypergraphs”(11261086);“On the disjoint path covers in graphs and related problems”(12261085)。

摘　　要：对简单的非完全图G和任意的正整数h,图G的h分支点连通度(h分支边连通度)是图G顶点子集(边子集)其删除呈现至少h个分支的最小基数.在此综述中,主要总结了一些关于h分支点连通度和h分支边连通度的一般性结论,以及一些熟知网络图的h分支点连通度和h分支边连通度的确切值.For a simple non-complete graph G,the h-component connectivity(resp.,h-component edge connectivity)of G is the minimum cardinality of a vertex subset of G whose deletion renders at least h components for any positive integer h.In this survey,we mainly summarize results on h-component connectivity(resp.,h-component edge connectivity)and the exact values of the h-component connectivity(resp.,h-component edge connectivity)of some well-known networks.

关 键 词：分支点连通度 分支边连通度 笛卡儿积 超立方体 

分 类 号：O157.5[理学—数学]