圈的k阶幂图的连通性研究  

Study on the Connectivity of the kth Power of Cycles

作　　者：李晓蓉 刘赛华[1] 

机构地区：[1]五邑大学数学与计算科学学院,广东 江门

出　　处：《理论数学》2024年第12期32-38,共7页Pure Mathematics

基　　金：国家自然科学基金青年项目(No.12201471)。

摘　　要：设G是连通图,G的k阶幂图Gk与G的顶点集相同且Gk中的两个顶点相邻当且仅当这两个顶点在G中的距离不大于k,本文给出了圈的幂图Cnk的点连通度κ(Cnk),边连通度λ(Cnk)和限制边连通度λ2(Cnk)。我们得到当1≤k⌊ n2⌋时,κ(Cnk)=λ(Cnk)=2k。关于限制边连通度,当n≥4时,λ2(Cnk)=2λ(Cnk)−2。Let G be a connected graph. The kth power Gkof G is a graph having the same vertex set of G such that the two vertices in Gkare adjacent if and only if the distance between the two vertices in G is less than or equal to k. In this paper, the connectivity κ(Cnk), edge connectivity λ(Cnk)and restricted edge connectivity λ2(Cnk)of Cnkare studied. We obtain the following results: κ(Cnk)=λ(Cnk)=2kwhen 1≤k⌊ n2⌋;λ2(Cnk)=2λ(Cnk)−2when n≥4.

关 键 词：幂图 连通度 边连通度 限制边连通度 

分 类 号：O15[理学—数学]