Distance Laplacian spectral ordering of sun type graphs

Abstract

Let G be a simple, connected graph of order n. Its distance Laplacian energy DLE(G) is given by DLE(G)=∑i=1n|ρiL−2W(G)n|, where ρ1L≥ρ2L≥⋯≥ρnL are the distance Laplacian eigenvalues and W(G) is the Wiener index of G. Distance Laplacian eigenvalues of sun and partial sun graphs have been characterized. We order the partial sun graphs by using their second largest distance Laplacian eigenvalue. Moreover, the distance Laplacian energy of sun and partial sun graphs have been derived in this paper. These graphs are also ordered by using their distance Laplacian energies.