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∈E √ d (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 bor index of a graph which is defined as the sum of the terms √ d (x) 2 + d(y) 2 where x is either adjacent or incident to y and x, y ∈ V ∪ E. We obtain exact values of this new topological index in some graph families. Some important properties of this index are obtained.