Aα-spectral radius of the second power of a graph

摘要

The kth power of a graph G, denoted by Gk, is a graph with the same set of vertices as G such that two vertices are adjacent in Gk if and only if their distance in G is at most k. In this paper, we give upper and lower bounds on the Aα-spectral radius of G2. Furthermore, the first three largest Aα-spectral radius of the second power of trees are determined.