Next Article in Journal
Asymptotic Expansion of the Modified Exponential Integral Involving the Mittag-Leffler Function
Previous Article in Journal
A Topological Coincidence Theory for Multifunctions via Homotopy
Open AccessArticle

Sharp Bounds on (Generalized) Distance Energy of Graphs

Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-3619995161, Shahrood, Iran
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea
Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(3), 426;
Received: 10 February 2020 / Revised: 4 March 2020 / Accepted: 11 March 2020 / Published: 16 March 2020
Given a simple connected graph G, let D ( G ) be the distance matrix, D L ( G ) be the distance Laplacian matrix, D Q ( G ) be the distance signless Laplacian matrix, and T r ( G ) be the vertex transmission diagonal matrix of G. We introduce the generalized distance matrix D α ( G ) = α T r ( G ) + ( 1 α ) D ( G ) , where α [ 0 , 1 ] . Noting that D 0 ( G ) = D ( G ) , 2 D 1 2 ( G ) = D Q ( G ) , D 1 ( G ) = T r ( G ) and D α ( G ) D β ( G ) = ( α β ) D L ( 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. View Full-Text
Keywords: distance energy; distance (signless) Laplacian energy; generalized distance energy; transmission regular graph distance energy; distance (signless) Laplacian energy; generalized distance energy; transmission regular graph
MDPI and ACS Style

Alhevaz, A.; Baghipur, M.; Das, K.C.; Shang, Y. Sharp Bounds on (Generalized) Distance Energy of Graphs. Mathematics 2020, 8, 426.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop