On the Generalized Distance Energy of Graphs

Alhevaz, Abdollah, Baghipur, Maryam, Ganie, Hilal Ahmad and Shang, Yilun (2019) On the Generalized Distance Energy of Graphs. Mathematics, 8 (1). p. 7. ISSN 2227-7390

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Official URL: https://doi.org/10.3390/math8010017

Abstract

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 - α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

Item Type: Article
Uncontrolled Keywords: Generalized distance matrix, distance signless Laplacian matrix, transmission regular graph, energy
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Elena Carlaw
Date Deposited: 19 Dec 2019 16:59
Last Modified: 19 Dec 2019 17:00
URI: http://nrl.northumbria.ac.uk/id/eprint/41766

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