Some upper and lower bounds for Dα-energy of graphs

Abdollah Alhevaz, Maryam Baghipur, Ebrahim Hashemi, Yilun Shang*

*Corresponding author for this work

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The generalized distance matrix of a connected graph G, denoted by Dα(G), is defined as (formula presented). Here, D(G) is the distance matrix and T r(G) represents the vertex transmissions. Let (formula presented) be the eigenvalues of Dα(G) and let W (G) be the n∑ Wiener index. The generalized distance energy of G can be defined as (formula presented) In this paper, we develop some new theory regarding the generalized distance energy E (G) for a connected graph G. We obtain some sharp upper and lower bounds for E (G) connecting a wide range of parameters in graph theory including the maximum degree ∆, the Wiener index W (G), the diameter d, the transmission degrees, and the generalized distance spectral spread DαS(G). We characterized the special graph classes that attain the bounds. i=1.

Original languageEnglish
Pages (from-to)73-86
Number of pages14
JournalJournal of Algebra Combinatorics Discrete Structures and Applications
Issue number2
Publication statusPublished - 10 May 2023

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