块为三角形的简单图的最小Hosoya指数  

Smallest Hosoya Index in Triangle-Block Graphs

作　　者：张深林[1] 

机构地区：[1]福建江夏学院数理教研部,福建福州350108

出　　处：《福建江夏学院学报》2015年第6期112-115,共4页Journal of Fujian Jiangxia University

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W_r是G_r∈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. Denote ζ as the set of simple connected graph with triangle blocks. Wr ∈ ζ is a graph consisting of r blocks. Wr ∈ ζ is a graph consisting of r blocks and with diameter of 2.By using the method of edge contraction and mathematical induction, the paper proves that Wr is the graph with the minimum Hosoya index in Gr ∈ζ .This statement is also valid for a graph with the number of connected component greater than 1.

关 键 词：匹配 HOSOYA指数 块 

分 类 号：O157.5[理学—数学]