繁星树线图的完美匹配数

On the number of perfect matchings in the line graph of a blossomed star

称一棵树T为繁星,如果它可以通过在星形树的悬挂点上添加一些悬挂边得到.给定两个正整数k和l满足k+l为偶数,令T_(k,l)表示由星形树S_(1,k)添加l条悬挂边而得到的所有繁星的集合.对任意的繁星T∈_(k,l),本文首先得到了其线图完美匹配数M(L(T))的表达式,然后通过引进一些变换,确定了M(L(T)),T∈_(k,l)的最小值和最大值.

A tree is called a blossomed star if it can be obtained by adding some pendant edges to pendant vertices of a star.Given two positive integers k and l such that k+l is even,let T_(k,l) denote the set of all blossomed stars obtained by adding l pendant edges to the star S_(1,k).In this paper,we first obtain the expression of the number of perfect matchings in the line graph of a blossomed star T,T∈_(k,l).Then by introducing some transformations,we determine minimum and maximum values of M(L(T)),T∈_(k,l).