一类图和偶圈的直积的超边连通度  

The Super Edge-Connectivity of Direct Product of a Family of Graph and an Even Cycle

作　　者：郭思佳 赵爽 王健 

机构地区：[1]太原理工大学数学学院,山西 晋中

出　　处：《应用数学进展》2024年第2期531-538,共8页Advances in Applied Mathematics

摘　　要：连通图G的超边连通度是指使得图G不连通且每个连通分支没有孤立点要删除的最少的边数,用表示。图G和H的直积,定义为G×H,是顶点集为V(G×H)=V(G)×V(H)的图,其中两个顶点(u1,v1)和(u2,v2)在G×H相邻当且仅当u1u2εE(G)且v1v2εE(H)。马天龙等人证明了G和完全图Kn的直积的超边连通度。本文证明了当n≥4且n为偶数时,一类图G和圈Cn的直积的超边连通度为。The super edge-connectivity of a connected graph G, denoted by , is the minimum number of edges whose deletion disconnects the graph such that each connected component has no isolated vertices. The direct product of graphs G and H, denoted by G×H , is the graph with vertex set V(G×H)=V(G)×V(H) , where two vertices (u1,v1) and (u2,v2) are adjacent in G×H if and only if u1u2εE(G) and v1v2εE(H) . Tianlong Ma et al. proved the super edge-connectivity of the direct product of G and complete graph. In this paper, it is proved that for a family of a graph G, where n≥4 and n is even.

关 键 词：边连通度 超边连通度 直积 

分 类 号：O15[理学—数学]