On the multiplicative sum Zagreb index of molecular graphs

Abstract

Multiplicative sum Zagreb index is a modified version of the famous Zagreb indices. For a graph GG, the multiplicative sum Zagreb index is defined as Π1*(G)=∏uv∈E(G)(dG(u)+dG(v)){\Pi }_{1}^{* }\left(G)={\prod }_{uv\in E\left(G)}\left({d}_{G}\left(u)+{d}_{G}\left(v)), where E(G)E\left(G) is the edge set of GG and dG(u){d}_{G}\left(u) stands for the degree of vertex uu in GG. In this article, we determine the extremal multiplicative sum Zagreb indices among all nn-vertex molecular trees, molecular unicyclic graphs, molecular bicyclic graphs and molecular tricyclic graphs.

Keywords

• multiplicative sum zagreb index
• molecular tree
• molecular unicyclic graphs
• molecular bicyclic graph
• molecular tricyclic graph
• 05c05
• 92e10