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).
Highlights
Let G V G, E G denote a graph whose set of vertices and set of edges are V G and E G, respectively
For any v ∈ V G, we denote the neighbors of v as NG v, and v NG v ∪ {v}
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
Summary
Let G V G , E G denote a graph whose set of vertices and set of edges are V G and E G , respectively. 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.
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