I形图的并的匹配等价图数

摘要

Two graphs G and H are said to be matching equivalent if they possess the same matching polynomials.δ(G) denotes the number of graphs which are matching equivalent to graph G. This paper lets Pn-2 be a path with vertices sequence x1,x2,,xn−2. In(n≥6) denotes the tree obtained from Pn−2 by adding pendant edges at vertices x2 and xn−3 , respectively. It computes the number of graphs of matching equivalent to the union graphs of I shape. Namely, δæ. è ç ö ø ÷iÎA Ii A is a repeated set of integers of great than or equal 6%两个图G和H 的匹配多项式相等，则称它们匹配等价。用δ(G)表示图G的所有不同构的匹配等价图的个数。In(n≥6)表示由路Pn-4的两个端点分别粘接一个P3的2度点后得到的图。计算了一些I形图并图的匹配等价图的个数，即δæèçöø÷iÎA Ii ，这里 A是一些大于等于6的整数组成的可重集。