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)

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.