平衡半传递有向图的弧连通性(英文)  

Arc Connectivity of Balanced Half-transitive Digraphs

作　　者：张崧[1] 田应智[1] 孟吉翔[1] 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）》2014年第1期22-25,共4页Journal of Xinjiang University(Natural Science Edition)

基　　金：supported by NSFC(11171283);Fund of Xinjiang University;Doctoral Fund of Xinjiang University

摘　　要：有向图D=(V,E)被称为是极大弧连通的,如果λ(D)=δ(D).此外,有向图D被称为是超弧连通的,如果每个最小的弧割都是其某个点的入弧集或者出弧集.以X1和X2为两部的一个有向二部图是半传递的,如果自同构群Aut(D)分别传递的作用在X1和X2上.在这篇论文中,证明了强连通的半传递有向图是极大弧连通的.还证明了除了少部分例外,连通半传递平衡有向图是超弧连通的.The digraph D=（V, E） is said to be maximally arc-connected, ifλ（D）=δ（D）. Moreover, the digraph D is said to be super arc-connected, if every minimum arc cut of D is the set of the in-arcs or the out-arcs of some vertex of D. A bipartite digraph D with bipartition X1 and X2 is half-transitive if Aut（D） acts transitively on X1 and X2, respectively. In this paper, we prove that each strongly connected half-transitive digraph is maximally arc-connected. Moreover, we prove that for all but a few exceptions, the connected half-transitive balanced digraph is super arc-connected.

关 键 词：非本原块 半传递有向图 极大弧连通 超弧连通 

分 类 号：O157.5[理学—数学]