On the spectral characterization of kite graphs

The Kite graph, denoted by Kite_p,q is obtained by appending a complete graph K_p to a pendant vertex of a path P_q. In this paper, firstly we show that no two non-isomorphic kite graphs are cospectral w.r.t the adjacency matrix. Let G be a graph which is cospectral with Kite_p,q and let w (G) be the clique number of G. Then, it is shown that w(G) ≥ p - 2q + 1. Also, we prove that Kite_p,2 graphs are determined by their adjacency spectrum.