块为三角形的简单图的最小Hosoya指数

摘要

一个图G的Hosoya指数是指图G中所有匹配的计数.用ζ表示块为三角形的简单连通图的集合,Gr∈ζ是ζ中块数为r的图,Wr∈ζ是ζ中直径为2,块数为r的图.利用边收缩法和数学归纳法可证Wr是Gr∈ζ中Hosoya指数最小的图.该结论在连通分支数大于1的图中也是成立的.%The Hosoya index of a graph G is defined as the number of matching in the graph G. Denoteζas the set of simple connected graph with triangle blocks.Wr∈ζis a graph consisting of r blocks.Wr∈ζis a graph consisting of r blocks and with diameter of 2.By using the method of edge contraction and mathematical induction, the paper proves thatWris the graph with the minimum Hosoya index inGr∈ζ.This statement is also valid for a graph with the number of connected component greater than 1.