On the spectral characterization of Kite graphs

Sezer Sorgun; Hatice Topcu

paper

On the spectral characterization of Kite graphs

arXiv:1506.01632

Abstract

The \textit{Kite graph}, denoted by $K i t e_{p, q}$ 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 $K i t e_{p, q}$ and the clique number of $G$ is denoted by $w (G)$ . Then, it is shown that $w (G) \geq p - 2 q + 1$ . Also, we prove that $K i t e_{p, 2}$ graphs are determined by their adjacency spectrum.