The Merrifield–Simmons index σ = σ(G) of a graph G is the number of independent vertex sets of G. This index can be calculated recursively and expressed in terms of Fibonacci numbers. We determine the molecular graphs for which σ can be recursively calculated in a single step.
The Merrifield-Simmons index of a graph is defined as the total number of its independent sets, including the empty set. Recently, Heuberger and Wagner ...
Let G be a (molecular) graph G. The Merrifield and Simmons index of G, denoted by or(G), is defined as the number of subsets of the vertex set V(G) in which ...
Oct 22, 2024 · The Merrifield-Simmons index of G, denoted by σ(G), is defined as the number of subsets of the vertex set V(G) in which no two vertices are ...
The Hosoya index and the Merrifield–Simmons index of a graph are defined as the total number of the matchings (including the empty edge set) and the total ...
The Merrifield–Simmons index of a graph is defined to be the number of inde- pendent sets in this graph. The Wiener index of a connected graph is the total.
People also ask
What is the difference between the Merrifield Simmons index and the Wiener index of graphs?
What is a connected graph graph theory?
What are the measures of connectedness in graphs?
What is the difference between a simple and a connected graph?
The Merrifield–Simmons index is the other topological index introduced by Merrifield and Simmons [15] in 1989. In [16] Gutman first named this index the ...
In this note we show that the Turán graph Tn(k) has the maximal Hosoya index and minimal Merrifield–Simmons index in Wn,k, and the minimal Hosoya index and ...
Abstract. For a graph G, the Merrifield-Simmons index i(G) is defined as the to- tal number of independent sets of the graph G. Let G(n, l, k) be the.
The graphs with the maximal Merrifield-Simmons index and the minimal Hosoya index, respectively, among the bicyclic graphs on n vertices with a given girth ...