Trees with Given Independence Number Maximizing the A -Spectral Radius

Abstract

Spectral graph theory is a widely studied and applied subject in combinatorial mathematics, computer science and social science. Nikiforov (2017) defined a convex linear combination for the graph G , denoted by. This concept can be regarded as a common generalization of adjacency matrix and unsigned Laplacian matrix. We mainly study the A  -spectral extreme problem for graphs, which is a generalization of Brualdi and Solheid's problem on A  -matrices. Let , n T  be the set of all trees with order n and independence number  . By graph transformations we determine the graphs with maximal A  -spectral radius among , n T  for /2 1 nn     . Therefore, we extend the results of Ji and Lu (2016) from spectral radius to A  -spectral radius.