Journal of Applied Mathematics
Volume 2012 (2012), Article ID 520156, 8 pages
http://dx.doi.org/10.1155/2012/520156
Research Article

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

Shaojun Dai1 and Ruihai Zhang2

1Department of Mathematics, Tianjin Polytechnic University, No. 399 Binshuixi Road, Xiqing District, Tianjin 300387, China
2Department of Mathematics, Tianjin University of Science and Technology, Tianjin 300457, China

Received 29 May 2012; Revised 18 June 2012; Accepted 27 June 2012

Academic Editor: Ferenc Hartung

Copyright © 2012 Shaojun Dai and Ruihai Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 ) .