Entire Sombor Index of Graphs

Let G = (V, E) be a simple graph with vertex set V and edge set E. The Sombor index of the graph G is a degree-based topological index, defined as ? SO(G) = uv & ISIN;E qd (u)2 + d(v)2, in which d(x) is the degree of the vertex x. In this paper, we introduce a new topological index called the entire Som-b or index of a graph which is defined as the sum of the terms \Id (x)2 + d(y)2 where x is either adjacent or incident to y and x, y & ISIN; V? E. We obtain exact values of this new topological index in some graph families. Some important properties of this index are obtained. ?c 2023 University of Kashan Press. All rights reserved