On complementary equienergetic strongly regular graphs

Harishchandra S. Ramane; K. Ashoka; Bolle Parvathalu; Daneshwari Patil; Ivan Gutman

Author(s)

Harishchandra S. Ramane Department of Mathematics, Karnatak University,580003 Dharwad,India

K. Ashoka Department of Mathematics, Karnatak University,580003 Dharwad,India

Bolle Parvathalu Department of Mathematics, Karnatak Arts College,580001 Dharwad,India

Daneshwari Patil Department of Mathematics, Karnatak University,580003 Dharwad,India

Ivan Gutman Faculty of Science, University of Kragujevac,P. O. Box 60, 34000 Kragujevac,Serbia

Abstract

The energy of a graph is the sum of absolute values of the eigenvalues of its adjacency matrix. Two graphs are said to be equienergetic if they have same energy. A graph is said to be complementary equienergetic if it is equienergetic with its complement. In this paper, we characterize the strongly regular graphs, which are complementary equienergetic. In addition, by means of Cartesian and strong graph products, we construct equienergetic graphs using complementary equienergetic graphs.

Publication Details

Page(s) 50-55

DOI DOI not available

Published Journal: Discrete Mathematics Letters, Volume: 4, Issue: 0, Year: 2020

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Keywords

equienergetic graphs, strongly regular graphs., complementary equienergetic graphs, energy of a graph

References

Adiga C.,Rakshith B. R. .2016 .On spectra of variants of the corona of two graphs and some new equienergetic graphs. Discuss. Math. Graph Theory, 36(1) : 127-140.

Ali A.,Elumalai S.,Mansour T.,Rostami M. A. .2020 .On the complementary equienergetic graphs. MATCH Commun. Math. Comput. Chem, 83 : 555-570.

Balakrishnan R. .2004 .The energy of a graph. Linear Algebra Appl, 387 : 287-295.

Bonifa A. S.,C. T. M. Vinagre A. S.,N. M. M. de Abreu A. S. .2008 .Constructing pairs of equienergetic and non-cospectral graphs Appl. , 21 : 338-341.

Brankov V.,I. Gutman V. .2004 .Equienergetic chemical trees. J. Serb. Chem. Soc, 69 : 549-553.

Colbourn C. J.,Dinitz J. H. .2007 .. , : .

Cvetkovic D. M.,Doob M.,Sachs H. .1980 .. Spectra of Graphs - Theory and Application, : .

Ganie H. A.,Pirzada S.,Iv A. .2014 .a´nyi, Energy, Laplacian energy of double graphs and new families of equienergetic graphs. Acta Univ. Sapientiae, Informatica, 6 : 89-116.

Godsil C.,Meagher K.,Ko-Rado Theorems .2016 .Erdo˝s-. , : .

I. Gutman .1978 .The energy of a graph. Ber. Math. Stat. Sekt. Forschungsz. Graz, 103 : 1-22.

Gutman I.,Furtula B. .2017 .The total -electron energy saga. Croat. Chem. Acta, 90 : 359-368.

Gutman I.,Polansky O. E. .1986 .. Organic Chemistry, : .

Harary F.,Addison-Wesley F. .1969 .. , : .

Horiguchi H.,Kitazume M.,Nakasora H.,European J.,Combin J. .2008 .The Hall-Janko graph and the Witt system W10. , 29 : 1-8.

Indulal G.,Vijayakumar A. .2006 .On pair of equienergetic graphs. MATCH Commun. Math. Comput. Chem, 55 : 83-90.

Indulal G.,Vijayakumar A. .2008 .Equienergetic self-complementary graphs. Czechoslovak Math. J, 58 : 911-919.

Li X.,Shi Y.,I. Gutman Y. .2012 .. , : .

Liu J.,Liu B. .2008 .On a pair of equienergetic graphs. MATCH Commun. Math. Comput. Chem, 59 : 275-278.

Ramane H. S.,Pal S.,Samanta A .2020 .. Handbook of Research on Advanced Applications of Graph Theory in Modern Society, : 267-296.

Ramane H. S.,Parvathalu B.,Patil D. D.,Ashoka K. .2019 .Graphs equienergetic with their complements. MATCH Commun. Math. Comput. Chem, 82 : 471-480.

Ramane H. S.,Walikar H. B. .2007 .Construction of equienergetic graphs. MATCH Commun. Math. Comput. Chem, 57 : 203-210.

Ramane H. S.,Walikar H. B.,Rao S. B.,Acharya B. D.,Hampiholi P. R.,Jog S. R.,I. Gutman S. R. .2004 .. , 26 : 5-13.

Ramane H. S.,Walikar H. B.,Rao S. B.,Acharya B. D.,Hampiholi P. R.,Jog S. R.,I. Gutman S. R. .2005 .Spectra and energies of iterated line graphs of regular graphs. , 18 : 679-682.

I. Stankovic´ ,D. .2009 .Stevanovic´, Small and not so small equienergetic graphs. MATCH Commun. Math. Comput. Chem, 61 : 443-450.

D. .2005 .Stevanovic´, Energy and. Linear Multilinear Algebra, 53 : 67-74.

Xu L.,Hou Y. .2007 .Equienergetic bipartite graphs. MATCH Commun. Math. Comput. Chem, 57 : 363-370.