路和圈、圈和圈的Kronecker积图的超点连通性  

Super Connected Kronecker Products of Paths, Cycles and Cycles

作　　者：吴丽芸 田应智[1] WU Liyun;TIAN Yingzhi(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）》2022年第2期176-181,共6页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金(11861066);新疆天山青年项目(2018Q066)。

摘　　要：如果图G的每一个最小点割都是某个点的邻点集,那么G是超点连通的,或者简称为是super-κ的.图G_(1)与G_(2)的Kronecker积图是一个点集为V(G_(1)×G_(2))=V(G_(1))×V(G_(2)),边集为E(G_(1)×G_(2))={(u_(1),v_(1))(u_(2),v_(2)):u_(1)u_(2)∈E(G_(1)),v_(1)v_(2)∈E(G_(2))}的图.本文证明了对整数m≥4和奇数n≥3,P_(m)×C_(n)是超点连通的;对整数m≥5和奇数n≥3,Cm×C_(n)是超点连通的.A graph G is super connected,or simply super-κ,if every minimum vertex-cut isolates a vertex.The Kronecker product G_(1)×G_(2) of graphs G_(1) and G_(2) is the graph with vertex set V(G_(1)×G_(2))=V(G_(1))×V(G_(2))and edge set E(G_(1)×G_(2))={(u_(1),v_(1))(u_(2),v_(2)):u_(1)u_(2)2 E(G_(1)),v_(1)v_(2) ∈E(G_(2))}.In this paper,we prove that P_(m)×C_(n) is super-κfor m≥4,n≥3 and n is odd;C_(m)×C_(n) is super-κfor m≥5,n≥3 and n is odd.

关 键 词：KRONECKER积 点连通度 极大点连通性 超点连通性 

分 类 号：O157.5[理学—数学]