中南民族大学学报（自然科学版）
中南民族大學學報（自然科學版）
중남민족대학학보（자연과학판）
JOURNAL OF SOUTH-CENTRAL UNIVERSITY FOR NATIONALITIES(NATURAL SCIENCE EDITION)
2011年
1期
109-112
,共4页
Hosoya指标%Merrifield-Simmons指标%围长
Hosoya指標%Merrifield-Simmons指標%圍長
Hosoya지표%Merrifield-Simmons지표%위장
Hosoya index%Merrifield-Simmons index%girth
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.
對于圖G,Hosoya指標和Merrifield-Simmons指標分彆定義為圖G中所有匹配的和及所有獨立集的和.θ-圖是通過剖分有公共頂點的3條平行邊而得到的圖.Θ(n,g)錶示圍長為g的n階θ-圖的集閤.得到Θ(n,g)中Hosoya指標和Merrifield-Simmons指標的最小值、最大值,併刻畫瞭相應的極值圖.
대우도G,Hosoya지표화Merrifield-Simmons지표분별정의위도G중소유필배적화급소유독립집적화.θ-도시통과부분유공공정점적3조평행변이득도적도.Θ(n,g)표시위장위g적n계θ-도적집합.득도Θ(n,g)중Hosoya지표화Merrifield-Simmons지표적최소치、최대치,병각화료상응적겁치도.
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.
