The general first Zagreb index conditions for Hamiltonian and traceable graphs

The general first Zagreb index of a graph G is defined as the sum of the αth powers of the vertex degrees of G, where α is a real number such that α = 0 and α = 1.In this paper, sufficient conditions involving the general first Zagreb index, with α > 1 or α < 0, are presented for the Hamiltonian and traceable graphs.