两类图的保Wiener指数的树  

Trees preserving Wiener index in two classes of graphs

作　　者：姜臻颖[1] 王力工[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072

出　　处：《纺织高校基础科学学报》2013年第2期176-182,共7页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金项目(11171273);国家级大学生创新创业训练计划项目资助(201210699107)

摘　　要：研究了两类图的保Wiener指数的树的存在性问题.Wiener指数W(G)是指一个连通图G中所有顶点对之间的距离之和.给定一个连通图G,若存在G中一棵子树T,使得W(G)=W(T),则称T为G的一棵保Wiener指数的树.定义了带悬挂边的双多扇形图S(s,t,l,k,s,t,l)及带悬挂边的组合多扇图G(s,t,l,m,k),利用图的Wiener指数的定义和性质,证明了图S(s,t,l,k,s,t,l)及图G(s,t,l,m,k)均有保Wiener指数的子树.The existence problem on trees preserving the Wiener index of two classes of graphs is studied in this paper. The Wiener index W（G） of a connected graph G is the sum of distances among all pairs of vertices in G. If there is a connected subtree T of a given connected graph G such that W（G）=W（T）, then T is called a preserving the Wiener index tree of G. In this paper, the graph S（s,t,l,k,s,t,l） is de- fined as a multi-fan graph with pendent edges and the graph G（s, t, l, re,k） is defined as a group of multi- fan graphs with pendent edges. By using the definition and the properties of Wiener index of a graph, it is proved that there exist subtrees preserving Wiener index in those two classes of graphs.

关 键 词：WIENER指数 树 距离 带悬挂边的多扇形图 

分 类 号：O157.5[理学—数学]