On the distance spectrum of windmill graphs

Abstract

The distance Laplacian matrix and the distance signless Laplacian matrix of a connected graph G are defined by LD(G) = TrG−D(G) and QD(G) = TrG + D(G). By a harmonious labelings of vertex set, the distance matrix of windmill graphs is described as a block matrix. In this paper, we obtain the eigenvalues and the corresponding eigenvectors of the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of windmill graphs .