ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH

The kite graph is denoted by Kiten,n-p which is obtained by appending a complete graph Kp to a pendant vertex of the path graph Pn-p . In this paper, we present some spectral properties of Laplacian matrix of the kite graph. First we give the Laplacian characteristic polynomial of Kiten,n-p , then we restrict its largest Laplacian eigenvalue depending on the clique number. Also we say that any connected graph which has the same clique number with Kiten,n-p is isomorphic to the Kiten,n-p under some conditions