CAJ | 학술논문

一个边割被称为圈边割,如果该边割能分离图的两个不同圈.如果一个图有圈边割,称该图为圈边可分离的.一个圈边可分离图G的最小圈边割的阶数被称为圈边连通度,记作cλA(G).定义:ζ(G)=min{ω(X)|导出G的最短圈},其中ω(X)为端点分别在X和V(G)-X中的边的数目.如果一个圈边可分离图G使得cλ(G)=ζ(G)成立,称该图是圈边最优的.Tian和Meng在文章[11]以及Yang et al在文章[15]中研究了两种不同的双轨道图的圈边最优性.本文我们将研究具有两个同阶轨道的双轨道图的圈边连通度.
일개변할피칭위권변할,여과해변할능분리도적량개불동권.여과일개도유권변할,칭해도위권변가분리적.일개권변가분리도G적최소권변할적계수피칭위권변련통도,기작cλA(G).정의:ζ(G)=min{ω(X)|도출G적최단권},기중ω(X)위단점분별재X화V(G)-X중적변적수목.여과일개권변가분리도G사득cλ(G)=ζ(G)성립,칭해도시권변최우적.Tian화Meng재문장[11]이급Yang et al재문장[15]중연구료량충불동적쌍궤도도적권변최우성.본문아문장연구구유량개동계궤도적쌍궤도도적권변련통도.
A cyclic edge-cut of a graph G is an edge set,the removal of which separates two cycles.If G has a cyclic edge-cut,then it is said to be cyclically separable.For a cyclically separable graph G,the cyclic edge-connectivity cλ(G)is the cardinality of a minimum cyclic edge-cut of G.Letζ(G)=min{ω(X)|X induces a shortest cycle in G},where ω(X)is the number of the edge with one end in X and the other one in V(G)-X.A cyclically separable graph G with cλ(G)= ζ(G)is said to be cyclically optimal.Tian and Meng in[11]and Yang et al in[15]studied the cyclically optimality of two kinds of double orbits graphs.In this work,we discuss the cyclic edge connectivityof graphs with two orbits of same size.