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

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.