论文信息 - The largest Hosoya index of (n, n+1)-graphs

The largest Hosoya index of (n, n+1)-graphs

The Hosoya index of a graph is defined as the total number of its matchings. In this paper, we obtain that the largest Hosoya index of (n,n+1)-graphs is f(n+1)+f(n-1)+2f(n-3), where f(n) is the nth Fibonacci number, and we characterize the extremal graphs.

Hanyuan Deng

[1] I. Gutmana,et al. Extremal Chemical Trees , 2002 .

[2] I. Gutman. Extremal hexagonal chains , 1993 .

[3] Dieter Rautenbach,et al. A note on the number of matchings and independent sets in trees , 2005, Discret. Appl. Math..

[4] Aimei YUa,et al. A Kind of Graphs with Minimal Hosoya Indices and Maximal Merrifield-Simmons Indices∗ , .

[5] Harold Ellsworth Tinnappel. On the topological index , 1952 .

[6] Yaoping Hou. On acyclic systems with minimal Hosoya index , 2002, Discret. Appl. Math..

[7] Hanyuan Deng,et al. The extremal unicyclic graphs with respect to Hosoya index and Merrifield-Simmons index , 2008 .

[8] Fuji Zhang,et al. On the ordering of graphs with respect to their matching numbers , 1986, Discret. Appl. Math..

[9] Stephan Wagner,et al. Extremal trees with respect to Hosoya Index and Merrifield-Simmons Index. ∗ , 2006 .

[10] H. Hosoya. Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons , 1971 .

[11] Feng Tian,et al. Extremal Catacondensed Benzenoids , 2003 .