极小循环图的圈点连通度  

Cyclic Vertex Connectivity of Minimal Circulant Graphs

作　　者：陈来焕 孟吉翔[2] 刘凤霞[2] 田应智[2] CHEN Laihuan;MENG Jixiang;LIU Fengxia;TIAN Yingzhi(College of Mathematics and Information Sciences,Henan University of Economics and Law.Zhengzhou 450003,China;College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China)

机构地区：[1]河南财经政法大学数学与信息科学学院,郑州450003 [2]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《应用数学学报》2019年第2期208-219,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11531011;11501487)资助项目

摘　　要：如果X-F中至少两个分支含圈,则称点集F为图X的一个圈点割.图X的所有圈点割的最小基数称为图x的圈点连通度,记为κ_c(X).在本文中,我们证明了极小循环图X=C(Z_n,S)在满足:(1)|S|≥2且对于a∈S有2a≡0(模n)或3α≡0(模n);或(2))|S|≥3且对任意的a∈S有2a■0(模n), 3a■0 (模n),则κ_c(X)=g(κ-2),其中g和κ(κ>2)分别为图X的围长和正则度.A vertex cut F of a graph X is called a cyclic vertex cut if at least two components of X-F contain cycles.The cyclic vertex connectivity of X,denoted by κc(X),is the minimum cardinality of all cyclic vertex cuts.In this paper,we show that,for the minimal circulant graph X=C(Zn,S),(1) if |S|≥2,and 2a≡0(mod n) or 3a≡0(mod n) for some a∈S,or (2) if |S|≥3,and 2a■0(mod n) and 3a■0(mod n) for any a∈S,then κc(G)=g(k-2),where g and k(k>2) are the girth and the regularity of X,respectively.

关 键 词：连通度 圈点割 圈点连通度 循环图 

分 类 号：O157.5[理学—数学]