由轮生成的Cayley图的广义3-连通度  

The Generalized 3-Connectivity of Cayley Graphs Generated by Wheel Graphs

作　　者：张燕 马木提·阿依古丽 ZHANG Yan;MAMUT Aygul(College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,Xinjiang)

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：《四川师范大学学报（自然科学版）》2020年第3期345-349,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11361060和11701492)。

摘　　要：令S?V(G),κG(S)表示图G中内部不交的S-树T1,T2,…,Tr的最大数目r,使得对任意i,j∈{1,2,…,r}且i≠j,有V(Ti)∩V(Tj)=S,E(Ti)∩E(Tj)=?.定义κk(G)=min{κG(S)|S?V(G),且|S|=k}为图G的广义k-连通度,其中k是整数,且2≤k≤n.令Sym(n)是在{1,2,…,n}上的对称群,T是Sym(n)的对换集合.G(T)表示点集是{1,2,…,n},边集是{ij|(ij)∈T}的图.若G(T)是一个轮图,则将Cayley图Cay(Sym(n),T)简记为WGn.主要研究由轮生成的Cayley图WGn的广义3-连通度,并证明κ3(WGn)=2n-3,其中n≥4.Let S?V(G) and κG(S) denote the maximum number r of internally disjoint S-trees T1,T2,…,Tr in graph G such that V(Ti)∩V(Tj)=S and E(Ti)∩E(Tj)=? for any i,j∈{1,2,…,r}and i≠j.For an integer k with 2≤k≤n,the generalized k-connectivity of a graph G is defined as κk(G)=min{κG(S)|S?V(G)and|S|=k}.Let Sym(n)be the symmetric group on{1,2,…,n}and T be a set of transpositions of Sym(n).Denote by G(T)the graph with vertex set{1,2,…,n}and edge set{ij|(ij)∈T}.If G(T)is a wheel graph,then simply denote the Cayley graph Cay(Sym(n),T)by WGn.In this paper,we study the generalized 3-connectivity of Cayley graphs generated by wheel graphs WGn,and prove that κ3(WGn)=2n-3,where n≥4.

关 键 词：CAYLEY图 广义k-连通度 内部不交的S-树 

分 类 号：O157.5[理学—数学]