Starlike trees whose maximum degree exceed 4 are determined by their Q-spectra

Abstract

Let A ( G ) and D ( G ) be the adjacency matrix and the degree matrix of a graph G , respectively. The matrix D ( G ) + A ( G ) is called the signless Laplacian matrix of G . The spectrum of the matrix D ( G ) + A ( G ) is called the Q-spectrum of G . A graph is said to be determined by its Q-spectrum if there is no other non-isomorphic graph with the same Q-spectrum. In this paper, we prove that all starlike trees whose maximum degree exceed 4 are determined by their Q-spectra.