Sharp bounds on (generalized) distance energy of graphs

Abdollah Alhevaz, Maryam Baghipur, Kinkar Ch. Das, Yilun Shang

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
9 Downloads (Pure)

Abstract

Given a simple connected graph G, let D(G) be the distance matrix, DL(G) be the distance Laplacian matrix, DQ(G) be the distance signless Laplacian matrix, and Tr(G) be the vertex transmission diagonal matrix of G. We introduce the generalized distance matrix Dα(G)=αTr(G)+(1−α)D(G) , where α∈[0,1] . Noting that D0(G)=D(G),2D12(G)=DQ(G),D1(G)=Tr(G) and Dα(G)−Dβ(G)=(α−β)DL(G) , we reveal that a generalized distance matrix ideally bridges the spectral theories of the three constituent matrices. In this paper, we obtain some sharp upper and lower bounds for the generalized distance energy of a graph G involving different graph invariants. As an application of our results, we will be able to improve some of the recently given bounds in the literature for distance energy and distance signless Laplacian energy of graphs. The extremal graphs of the corresponding bounds are also characterized.
Original languageEnglish
Article number426
JournalMathematics
Volume8
Issue number3
DOIs
Publication statusPublished - 16 Mar 2020

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