Θ(n,g)中关于Hosoya指标和Merrifield-Simmons指标的极值θ-图(英文)  

Extremal θ-Graphs with Respect to Hosoya Index and Merrifield-Simmons Index in Θ(n,g)

作　　者：朱忠熏[1] 

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2011年第1期109-112,共4页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(61070197);中南民族大学中央高校基本科研业务费专项资金资助项目(CZQ10007)

摘　　要：对于图G,Hosoya指标和Merrifield-Simmons指标分别定义为图G中所有匹配的和及所有独立集的和.θ-图是通过剖分有公共顶点的3条平行边而得到的图.Θ(n,g)表示围长为g的n阶θ-图的集合.得到了Θ(n,g)中Hosoya指标和Merrifield-Simmons指标的最小值、最大值,并刻画了相应的极值图.For a graph G,the Hosoya index and the Merrifield-Simmons index are defined as the total number of its matchings and its independent sets,respectively.The θ-graph is obtained by subdividing the edges of the multigraph consisting of 3 parallel edges. Let Θ（n,g） be the set of θ-graphs with given girth g and order n.In this paper,we obtain the smallest and the largest Hosoya index and Merrifield-Simmons index in Θ（n,g）,respectively.At the same time,we characterize the corresponding extremal graphs.

关 键 词：HOSOYA指标 MERRIFIELD-SIMMONS指标 围长 

分 类 号：O157[理学—数学]