## Journal of Applied Mathematics

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

### The Merrifield-Simmons Index and Hosoya Index of $C(n,k,\lambda )$ Graphs

#### Abstract

The Merrifield-Simmons index $\mathrm{i(G)}$ 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 $\mathrm{z(G)}$ of a graph $G$ is defined as the total number of independent edge subsets, that is, the total number of its matchings. By $C(n,k,\lambda )$ we denote the set of graphs with $n$ vertices, $k$ cycles, the length of every cycle is $\lambda $, 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 $\mathrm{i(G)}$ and the Hosoya index $\mathrm{z(G)}$ for a graph $G$ in $C(n,k,\lambda )$.

#### 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