Seidel Equienergetic Graphs

Ramane, Harishchandra S.; Gundloor, Mahadevappa M.; Hosamani, Sunilkumar M.

doi:10.18052/www.scipress.com/BMSA.16.62

BMSA > BMSA Volume 16 > Seidel Equienergetic Graphs

< Back to Volume

Seidel Equienergetic Graphs

Full Text PDF

Abstract:

The Seidel matrix S(G) of a graph G is the square matrix with diagonal entries zeroes and off diagonal entries are – 1 or 1 corresponding to the adjacency and non-adjacency. The Seidel energy SE(G) of G is defined as the sum of the absolute values of the eigenvalues of S(G). Two graphs G₁ and G₂ are said to be Seidel equienergetic if SE(G₁) = SE(G₂). We establish an expression for the characteristic polynomial of the Seidel matrix and for the Seidel energy of the join of regular graphs. Thereby construct Seidel non cospectral, Seidel equienergetic graphs on n vertices, for all n ≥ 12

Info:

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 16)

Pages:

62-69

DOI:

https://doi.org/10.18052/www.scipress.com/BMSA.16.62

Citation:

H. S. Ramane et al., "Seidel Equienergetic Graphs", Bulletin of Mathematical Sciences and Applications, Vol. 16, pp. 62-69, 2016

Online since:

August 2016

Authors:

Harishchandra S. Ramane, Mahadevappa M. Gundloor, Sunilkumar M. Hosamani

Keywords:

Join of Graphs, Seidel Eigenvalues, Seidel Energy

Export:

RIS, BibTeX, Text

Distribution:

Open Access

This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

[1] C. Adiga, R. Balakrishnan, W. So, The skew energy of digraphs, Linear Algebra Appl. 432 (2010) 1825-1835.

[2] R. Balakrishnan, The energy of a graph, Linear Algebra Appl. 387 (2004) 287-295.

[3] M. A. Bhat, S. Pirzada, On equienergetic signed graphs, Discrete Appl. Math. 189 (2015) 1-7.

[4] A. S. Bonifacio, C. T. M. Vinagre, N. M. M. de Abreu, Constructing pairs of equienergetic and non-cospectral graphs, Appl. Math. Lett. 21 (2008) 338-341.

DOI: https://doi.org/10.1016/j.aml.2007.04.002

[5] V. Brankov, D. Stevanovic, I. Gutman, Equienergetic chemical trees, J. Serb. Chem. Soc. 69 (2004) 549-553.

DOI: https://doi.org/10.2298/jsc0407549b

[6] A. E. Brouwer, W. H. Haemers, Spectra of Graphs, Springer, Berlin, (2012).

[7] D. M. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs, Academic Press, New York, (1980).

[8] H. A. Ganie, S. Pirzada, A. Ivanyi, Energy, Laplacian energy of double graphs and new families of equienergetic graphs, Acta Univ. Sapientiae Info. 6 (2014) 89-116.

DOI: https://doi.org/10.2478/ausi-2014-0020

[9] K. A. Germina, K. S. Hameed, On signed paths, signed cycles and their energies, Appl. Math. Sci. 4 (2010) 3455-3466.

[10] K. A. Germina, K. S. Hameed, T. Zaslavsky, On product and line graphs of signed graphs, their eigenvalues and energy, Linear Algebra Appl. 435 (2011) 2432-2450.

DOI: https://doi.org/10.1016/j.laa.2010.10.026

[11] E. Ghorbani, On eigenvalues of Seidel matrices and Haemers conjecture, arXiv: 1301. 0075v1.

[12] I. Gutman, The energy of a graph, Ber. Math. Stat. Sekt. Forschungsz. Graz 103 (1978) 1-22.

[13] W. H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem. 68 (2012) 653-659.

[14] G. Indulal, I. Gutman, A. Vijaykumar, On the distance energy of a graph, MATCH Commun. Math. Comput. Chem. 60 (2008) 473-484.

[15] G. Indulal, A. Vijaykumar, Equienergetic self-complementary graphs, Czechoslovak Math. J. 58 (2008) 451-461.

[16] X. Li, Y. Shi, I. Gutman, Graph Energy, Springer, New York, (2012).

[17] W. Lopez, J. Rada, Equienergetic digraphs, Int. J. Pure Appl. Math. 36 (2007) 361-372.

[18] Nageswari, P. B. Sarasija, Seidel energy and its bounds, Int. J. Math. Analysis 8 (2014) 2869-2871.

DOI: https://doi.org/10.12988/ijma.2014.410309

[19] N. G. Nayak, Equienergetic net-regular signed graphs, Int. J. Contemp. Math. 9 (2014) 685-693.

[20] M. R. Oboudi, Energy and Seidel energy of graphs, MATCH Commun. Math. Comput. Chem. 75 (2016) 291-303.

[21] S. Pirzada, M. A. Bhat, Energy of signed digraphs, Discrete Appl. Math. 169 (2014) 195-205.

DOI: https://doi.org/10.1016/j.dam.2013.12.018

[22] H. S. Ramane, I. Gutman, M. M. Gundloor, Seidel energy of iterated line graphs of regular graphs, Kragujevac J. Math. 39 (2015) 7-12.

DOI: https://doi.org/10.5937/kgjmath1501007r

[23] H. S. Ramane, I. Gutman, D. S. Revankar, Distance equienergetic graphs, MATCH Commun. Math. Comput. Chem. 60 (2008) 473-484.

[24] H. S. Ramane, I. Gutman, H. B. Walikar, S. B. Halkarni, Equienergetic complement graphs, Kragujevac J. Sci. 27 (2005) 67-74.

[25] H. S. Ramane, K. C. Nandeesh, I. Gutman, X. Li, Skew equienergetic digraphs, Trans. Comb. 5 (2016) 15-23.

[26] H. S. Ramane, D. S. Revankar, I. Gutman, H. B. Walikar, Distance spectra and distance energies of iterated line graphs of regular graphs, Publ. Inst. Math. (Beograd) 85 (2009) 39-46.

DOI: https://doi.org/10.2298/pim0999039r

[27] H. S. Ramane, H. B. Walikar, Construction of equienergetic graphs, MATCH Commun. Math. Comput. Chem. 57 (2007) 203-210.

[28] H. S. Ramane, H. B. Walikar, S. B. Rao, B. D. Acharya, P. R. Hampiholi, S. R. Jog, I. Gutman, Equienergetic graphs, Kragujevac J. Math. 26 (2004) 5-13.

DOI: https://doi.org/10.1016/j.aml.2004.04.012

[29] H. S. Ramane, H. B. Walikar, S. B. Rao, B. D. Acharya, P. R. Hampiholi, S. R. Jog, I. Gutman, Spectra and energies of iterated line graphs of regular graphs, Appl. Math. Lett. 18 (2005) 679-682.

DOI: https://doi.org/10.1016/j.aml.2004.04.012

[30] D. Stevanovic, Energy and NEPS of graphs, Lin. Multilin. Algebra 53 (2005) 67-74.

[31] L. Xu, Y. Hou, Equienergetic bipartite graphs, MATCH Commun. Math. Comput. Chem. 57 (2007) 363-370.

Show More Hide

Cited By:

[1] H. Ramane, B. Parvathalu, K. Ashoka, D. Patil, "On A-energy and S-energy of certain class of graphs", Acta Universitatis Sapientiae, Informatica, Vol. 13, p. 195, 2021