The Merrifield-Simmons index of a graph 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 The Hosoya index of a graph is defined as the total number of independent edge subsets, that is, the total number of its matchings. By we denote the set of graphs with vertices, cycles, the length of every cycle is , 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 and the Hosoya index for a graph in .
Shaojun Dai. Ruihai Zhang. "The Merrifield-Simmons Index and Hosoya Index of Graphs." J. Appl. Math. 2012 1 - 8, 2012. https://doi.org/10.1155/2012/520156