The $\alpha$–Sombor index and some Hamiltonian properties of graphs

Let G = (V, E) be a graph.For a positive real number , the -Sombor index of G is defined as uvE (d (u) + d (v)) 1/ , where d(u) and d(v) denote the degrees of vertices u and v in G, respectively.In this article, an upper bound for the -Sombor index of a graph is presented.Sufficient conditions involving the -Sombor index for some Hamiltonian properties of graphs are also given.