同阶双轨道连通图的超圈边连通性  

Super cyclically edge connected graphs with two orbits of the same size

作　　者：姜海宁[1] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《上海大学学报（自然科学版）》2017年第2期252-256,共5页Journal of Shanghai University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11471273)

摘　　要：对于图G,如果G-F是不连通的且至少有两个分支含有圈,则称F为图G的圈边割.如果图G有圈边割,则称其为圈可分的.最小圈边割的基数叫作圈边连通度.如果去除任何一个最小圈边割,总存在一分支为最小圈,则图G为超圈边连通的.设G=(G_1,G_2,(V_1,V_2))为双轨道图,最小度δ(G)≥4,围长g(G)≥6且|V_1|=|V_2|.假设G_i是k_i-正则的,k_1≤k_2且G_1包含一个长度为g的圈,则G是超圈边连通的.For a graph G, an edge set F is a cyclic edge-cut if （G - F） is disconnected and at least two of its components contain cycles. If G has a cyclic edge-cut, it is said to be cyclically separable. The cyclic edge-connectivity is cardinality of a minimum cyclic edgecut of G. A graph is super cyclically edge-connected if removal of any minimum cyclic edge-cut makes a component a shortest cycle. Let G = （G1,G2, （V1,V2）） be a doubleorbit graph with minimum degree δ（G） ≥ 4, girth g ≥ 6 and ｜V1｜ = ｜V2｜. Suppose Gi is ki-regular, kl ≤ k2 and G1 contains a cycle of length g, then G is super cyclically edge connected.

关 键 词：圈边割 圈边连通度 超圈边连通性 轨道 

分 类 号：O157.5[理学—数学]