On the complementary equienergetic graphs

Akbar Ali, Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami

Research output: Contribution to journalArticlepeer-review


Energy of a simple graph G, denoted by ∈(G), is the sum of the absolute values of the eigenvalues of G. Two graphs with the same order and energy are called equienergetic graphs. A graph G with the property G ≅ G is called selfcomplementary graph, where G denotes the complement of G. Two non-selfcomplementary equienergetic graphs G1and G2satisfying the property G1≅ G2are called complementary equienergetic graphs. Recently, Ramane et al. [Graphs equienergetic with their complements, MATCH Commun. Math. Comput. Chem. 82 (2019) 471-480] initiated the study of the complementary equienergetic regular graphs and they asked to study the complementary equienergetic non-regular graphs. In this paper, by developing some computer codes and by making use of some software like Nauty, Maple and GraphTea, all the complementary equienergetic graphs with at most 10 vertices as well as all the members of the graph class Ω ={G: ∈(L(G)) = 'Equation Presented', the order of G is at most 10} are determined, where L(G) denotes the line graph of G. In the cases where we could not find the closed forms of the eigenvalues and energies of the obtained graphs, we verify the graph energies using a high precision computing (2000 decimal places) of Maple. A result about a pair of complementary equienergetic graphs is also given at the end of this paper.

Original languageEnglish
Pages (from-to)555-570
Number of pages16
Issue number3
StatePublished - 2020

Bibliographical note

Funding Information:
Acknolwedgmen: tSurseh Elumalai’s reseahrcis supported by Unievrsiytof Haifa, Israel, for the Postdctorao l studies and it is gratefully acknowledged.

Funding Information:
Suresh Elumalai's research is supported by University of Haifa, Israel, for the Postdoctoral studies and it is gratefully acknowledged.

Publisher Copyright:
© 2020 University of Kragujevac, Faculty of Science. All rights reserved.

ASJC Scopus subject areas

  • Chemistry (all)
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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