摘要

Let G be an unicycle graph and d(nu) the degree of the vertex v. In this paper, we investigate the following topological indices for an unicycle graph G: alpha(m) (G) = Sigma(nu is an element of V(G)) d(nu) (m), alpha(-m)(G) = Sigma(nu is an element of V(G)) d(nu)(-m), alpha(-1/m)= Sigma(nu is an element of V(G)) d(nu) (-1/m), where m >= 2 is an integer. All unicycle graphs with the largest values of the three topological indices are characterized.