On the Hosoya index of graphs  

作　　者：WANG Bo YE Cheng-fu YAN Li-ying 

机构地区：[1]Department of Mathematics, Qinghai Normal University, Xining 810008, China [2]Qinghai Communications Technical College, Xining 810003, China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2010年第2期155-161,共7页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(10761008, 10461009);the Science Foundation of the State Education Ministry of China(205170)

摘　　要：Let G be a （molecular） graph. The Hosoya index Z（G） of G is defined as the number of subsets of the edge set E（G） in which no two edges are adjacent in G, i.e., Z（G） is the total number of matchings of G. In this paper, we determine all the connected graphs G with n ＋ 1 ≤ Z（G） ≤5n - 17 for n ≥ 19. As a byproduct, the graphs of n vertices with Hosoya index from the second smallest value to the twenty first smallest value are obtained for n ≥ 19.Let G be a （molecular） graph. The Hosoya index Z（G） of G is defined as the number of subsets of the edge set E（G） in which no two edges are adjacent in G, i.e., Z（G） is the total number of matchings of G. In this paper, we determine all the connected graphs G with n ＋ 1 ≤ Z（G） ≤5n - 17 for n ≥ 19. As a byproduct, the graphs of n vertices with Hosoya index from the second smallest value to the twenty first smallest value are obtained for n ≥ 19.

关 键 词：GRAPH Hosoya index MATCHING 

分 类 号：TP311.13[自动化与计算机技术—计算机软件与理论] TS210.9[自动化与计算机技术—计算机科学与技术]