On the distance Laplacian energy ordering of a tree

摘要

For a simple connected graph G of order n having distance Laplacian eigenvalues ρ1L≥ρ2L≥⋯≥ρnL, the distance Laplacian energy DLE(G) is defined as DLE(G)=∑i=1n|ρiL−2W(G)n|, where W(G) is the Weiner index of G. In this paper, we describe the distance Laplacian eigenvalues of a tree of diameter 3. We discuss the distance Laplacian energy of trees of diameter 3 and show that like the Laplacian energy [31] these trees can be ordered on the basis of their distance Laplacian energy. As application we obtain an upper bound for the distance Laplacian energy of a connected graph.