k正则点传递二部图的超圈边连通性  

Hyper-cyclic Edge Connectivity of K-regular Point Transitive Bipartite Graphs

作　　者：万海云 姜海宁 WAN Hai-yun;JIANG Hai-ning(Department of Public Education,Heze Medical College,Heze Shandong 274000,China;School of Mathematics and Statistics,Heze University,Heze Shandong 274015,China)

机构地区：[1]菏泽医学专科学校公共教学部,山东菏泽274000 [2]菏泽学院数学与统计学院,山东菏泽274015

出　　处：《菏泽学院学报》2024年第5期22-25,共4页Journal of Heze University

基　　金：国家自然科学基金(12061007)。

摘　　要：如果删除一个图G的边集E后,至少有两个连通分支有圈,则称E为图G的圈边割,把有圈边割的图称为圈可分的.对于一个圈可分图G来说,最小圈边割的基数称为圈边连通度λc(G).如果去除任何一个最小圈边割,总存在一连通分支为最小圈,则图G为超圈边连通的.利用反证法,得到一个(k≥4)正则围长g(G)≥6的点传递二部图是超圈边连通的.If deleting the edge set E of a graph G,there are at least two connected branches with loops,then E is called the edge cut of graph G,and the graph with edge cuts is called separable.For a separable graph G,the cardinality of the minimum circle edge cut is called the circle edge connectivityλc(G).If any minimum loop edge cut is removed,there will always be a connected branch that is the minimum loop,and then graph G is hyper loop edge connected.Using the method of proof by contradiction,it is found that k(≥4)regular bipartite graph with a circumference of g(G)≥6 is hyper-cyclic edge connected.

关 键 词：圈边连通度 圈边割 超圈边连通性 轨道 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]