具有完美匹配树图的外围维纳指标的上(下)界

Upper and lower bounds for the peripheral Wiener indices of trees with a perfect matching

设T为具有n个顶点的树图,树图T的外围维纳指标为T中所有外围顶点对之间的距离之和,即PW(T)=∑{u,v}■P(T)d(u,v),其中P(T)为树图的所有外围顶点构成的集合.本文分别给出了具有完美匹配的树图的外围维纳指标的上界和下界,以及外围顶点数给定的具有完美匹配的树图的外围维纳指标的上界和下界.

Let T be a tree of order n.The peripheral Wiener index of T is the sum of the distances between all peripher-al vertex pairs,i.e.,PW(T)=∑{u,v}■P(T)d(u,v),where P(T)is the set of all peripheral vertices of T.In this paper,the up-per and lower bounds of the peripheral Wiener indices for trees with a perfect matching are determined,as well as the trees with perfect matching and a given number of peripheral vertices.