ON THE PRODUCT OF GEOMETRIC-ARITHMETIC, SOMBOR AND FIRST ZAGREB INDICES

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.