On the spectral characterization of Kite graphs

The $\mathit{\text{Kite}}\mathit{\text{graph}}$, denoted by $Kit{e}_{p,q}$ 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 adjacency matrix. Let $G$ be a graph which is cospectral with $Kit{e}_{p,q}$ and the clique number of $G$ is denoted by $w(G)$. Then, it is shown that $w(G)\geq p-2q+1$\mathrm{.}Also,weprovethat$Kite_{p,2}$ graphs are determined by their adjacency spectrum.