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

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K_n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C_n的直积的超边连通度为。

Abstract: 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.