On the distance Laplacian energy ordering of a tree

Hilal A. Ganie

Applied Mathematics and Computation, 2021, vol. 394, issue C

Abstract: 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.

Keywords: Distance matrix; Distance Laplacian matrix; Distance Laplacian energy (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:394:y:2021:i:c:s0096300320307153

DOI: 10.1016/j.amc.2020.125762

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