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.