On families of graphs which are both adjacency equienergetic and distance equienergetic

Title

On families of graphs which are both adjacency equienergetic and distance equienergetic

Creator

Ramane H.S.; Parvathalu B.; Ashoka K.; Pirzada S.

Description

Let A(G) and D(G) be the adjacency and distance matrices of a graph G respectively. The adjacency energy or A-energy EA(G) of a graph G is defined as the sum of the absolute values of the eigenvalues of A(G). Analogously, the D-energy ED(G) is defined to be the sum of the absolute values of the eigenvalues of D(G). One of the interesting problems on graph energy is to characterize those graphs which are equienergetic with respect to both the adjacency and distance matrices. A weaker problem is to construct the families of graphs which are equienergetic with respect to both the adjacency and distance matrices. In this paper, we find the explicit relations between A-energy and D-energy of certain families of graphs. As a consequence, we provide an answer to the above open problem (Indulal in https://icgc2020.wordpress.com/invitedlectures, 2020; http://www.facweb.iitkgp.ac.in/rkannan/gma.html, 2020) The Indian National Science Academy 2022.

Source

Indian Journal of Pure and Applied Mathematics, Vol-55, No. 1, pp. 198-209.

Date

2024-01-01

Publisher

Indian National Science Academy

Subject

05C50; 05C76; Distance energy; Distance equienergetic graphs; Equienergetic graphs; Graph energy

Coverage

Ramane H.S., Department of Mathematics, Karnatak University, Karnataka, Dharwad, 580003, India; Parvathalu B., Department of Mathematics, Christ University, Karnataka, Bangalore, 560029, India; Ashoka K., Department of Mathematics, Karnatak Universitys Karnatak Arts College, Karnataka, Dharwad, 580001, India; Pirzada S., Department of Mathematics, University of Kashmir, Kashmir, Srinagar, 190006, India

Rights

Restricted Access

Relation

ISSN: 195588

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1007/s13226-022-00355-1

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85143701097&doi=10.1007%2fs13226-022-00355-1&partnerID=40&md5=7c0a408480b326b1f4ad06c806c44217