Journal of Applied Mathematics

The Merrifield-Simmons Index and Hosoya Index of C ( n , k , λ ) Graphs

Shaojun Dai and Ruihai Zhang

Full-text: Open access

Abstract

The Merrifield-Simmons index i(G) of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, that is, the number of independent vertex sets of G The Hosoya index z(G) of a graph G is defined as the total number of independent edge subsets, that is, the total number of its matchings. By C ( n , k , λ ) we denote the set of graphs with n vertices, k cycles, the length of every cycle is λ , and all the edges not on the cycles are pendant edges which are attached to the same vertex. In this paper, we investigate the Merrifield-Simmons index i(G) and the Hosoya index z(G) for a graph G in C ( n , k , λ ) .

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 520156, 8 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495220

Digital Object Identifier
doi:10.1155/2012/520156

Mathematical Reviews number (MathSciNet)
MR2948171

Zentralblatt MATH identifier
1255.05133

Citation

Dai, Shaojun; Zhang, Ruihai. The Merrifield-Simmons Index and Hosoya Index of $C(n,k,\lambda )$ Graphs. J. Appl. Math. 2012 (2012), Article ID 520156, 8 pages. doi:10.1155/2012/520156. https://projecteuclid.org/euclid.jam/1355495220


Export citation