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, i.e., the number of independent vertex sets of G . In this paper, we determine the minimum Merrifield–Simmons index of unicyclic graphs with n vertices and diameter at most four.
Highlights
Numerous topological and chemical indices have been used for analyzing molecular graphs ([1,2,3,4]). e Merrifield–Simmons index was introduced by Merrifield and Simmons [5] in 1989.is index is one of the topological indices whose mathematical properties turned out to be applicable to several questions of molecular chemistry
E 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, i.e., the number of independent vertex sets of G
Trees, unicyclic graphs, and certain structures involving pentagonal and hexagonal cycles are of major interest [7,8,9,10,11,12,13,14,15]
Summary
Numerous topological and chemical indices have been used for analyzing molecular graphs ([1,2,3,4]). e Merrifield–Simmons index was introduced by Merrifield and Simmons [5] in 1989. Numerous topological and chemical indices have been used for analyzing molecular graphs ([1,2,3,4]). E Merrifield–Simmons index was introduced by Merrifield and Simmons [5] in 1989. Is index is one of the topological indices whose mathematical properties turned out to be applicable to several questions of molecular chemistry. E 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, i.e., the number of independent vertex sets of G. Several papers deal with the Merrifield–Simmons index in several given graph classes. We investigate the Merrifield–Simmons index i(G) of unicyclic graphs with diameter at most four.
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