Abstract

Assume $\Omega$ is a connected and simple graph with edge set $E(\Omega)$ and vertex set $V(\Omega)$. In chemical graph theory, the Geometric-Arithmetic index, Sombor index, and first Zagreb index of graph are three well-defined and studied topological indices. In the present study, we introduce the new graph invariant, we call it as $GSM(\Omega)$ index, this new graph invariant is the product of Geometric-Arithmetic index, Sombor index, and first Zagreb index. Furthermore we discuss the effect on $GSM(\Omega)$ of inserting and deleting an edge into a graph $\Omega$. In addition, we investigate the connections between the GSM(G) index and various well-studied topological indices.

Keywords and Phrases

Topological indices, maximum and minimum degree, degree (of vertex).

A.M.S. subject classification

05C07, 05C09, 05C92.

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