Generalized Topological Indices Of Unicycle Graphs

Let G — (V, E) be a simple and connected graph with the vertex set V and the edge set E. The four generalized topological indices for G are defined as the followingwhere d_v is the degree of vertex v and m ≥ 2 is an integer. The four topological indices of G are generalized from the zeroth-order Randic index:and the first zagreb index:In this paper, we investigate the four generalized topological indices through the method of graph transformations. All unicycle graphs with the first three largest values and the first three smallest values of the four generalized topological indices are characterized.