Opuscula Math. 38, no. 1 (2018), 5-13
https://doi.org/10.7494/OpMath.2018.38.1.5

 
Opuscula Mathematica

Upper bounds for the extended energy of graphs and some extended equienergetic graphs

Chandrashekar Adiga
B. R. Rakshith

Abstract. In this paper, we give two upper bounds for the extended energy of a graph one in terms of ordinary energy, maximum degree and minimum degree of a graph, and another bound in terms of forgotten index, inverse degree sum, order of a graph and minimum degree of a graph which improves an upper bound of Das et al. from [On spectral radius and energy of extended adjacency matrix of graphs, Appl. Math. Comput. 296 (2017), 116-123]. We present a pair of extended equienergetic graphs on \(n\) vertices for \(n\equiv 0(\text{mod } 8)\) starting with a pair of extended equienergetic non regular graphs on \(8\) vertices and also we construct a pair of extended equienergetic graphs on \(n\) vertices for all \(n\geq 9\) starting with a pair of equienergetic regular graphs on \(9\) vertices.

Keywords: energy of a graph, extended energy of a graph, extended equienergetic graphs.

Mathematics Subject Classification: 05C50.

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  1. C. Adiga, B.R. Rakshith, On spectra of variants of the corona of two graphs and some new equienergetic graphs, Discuss. Math. Graph Theory 36 (2016), 127-140.
  2. R. Balakrishnan, The energy of a graph, Linear Algebra Appl. 387 (2004), 287-295.
  3. V. Brankov, D. Stevanović, I. Gutman, Equienergetic chemical trees, J. Serb. Chem. Soc. 69 (2004), 549-553.
  4. A.E. Brouwer, W.H. Haemers, Spectra of Graphs, Springer, Berlin, 2012.
  5. D. Cvetković, M. Doob, H. Sachs, Spectra of Graphs: Theory and Application, Academic Press, New York, 1980.
  6. K.Ch. Das, I. Gutman, B. Furtula, On spectral radius and energy of extended adjacency matrix of graphs, Appl. Math. Comput. 296 (2017), 116-123.
  7. W.L. Ferrar, A Text-Book of Determinants, Matrices and Algebraic Forms, Oxford University Press, 1953.
  8. B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015) 4, 1184-1190.
  9. S. Gong, X. Li, G. Xu, I. Gutman, B. Furtula, Borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 74 (2015), 321-332.
  10. I. Gutman, The energy of a graph, Ber. Math. Statist. sekt. Forschungsz. Graz. 103 (1978), 1-22.
  11. G. Indulal, A. Vijayakumar, On a pair of equienergetic graphs, MATCH Commun. Math. Comput. Chem. 55 (2006), 83-90.
  12. X. Li, Y. Shi, I. Gutman, Graph Energy, Springer, New York, 2012.
  13. X. Li, M. Wei, S. Gong, A computer search for the borderenergetic graphs of order 10, MATCH Commun. Math. Comput. Chem. 74 (2015), 333-342.
  14. J. Liu, B. Liu, On a pair of equienergetic graphs, MATCH Commun. Math. Comput. Chem. 59 (2008), 275-278.
  15. A.W. Marshall, I. Olkin, B.C. Arnold, Inequalities: Theory of Majorization and its Applications, Springer, New York, 2011.
  16. S. Mukwembi, On diameter and inverse degree of a graph, Discrete Math. 310 (2010), 940-946.
  17. H.S. Ramane, H.B. Walikar, Construction of equienergetic graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), 203-210.
  18. H.S. Ramane, I. Gutman, H.B. Walikar, S.B. Halkarni, Equienergetic complement graphs, Kragujevac J. Sci. 27 (2005), 67-74.
  19. L. Xu, Y. Hou, Equienergetic bipartite graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), 363-370.
  20. Y.Q. Yang, L. Xu, C.Y. Hu, Extended adjacency matrix indices and their applications, J. Chem. Inf. Comput. Sci. 34 (1994), 1140-1145.
  • Chandrashekar Adiga
  • University of Mysore, Manasagangothri, Department of Studies in Mathematics, Mysuru - 570 006, India
  • B. R. Rakshith
  • University of Mysore, Manasagangothri, Department of Studies in Mathematics, Mysuru - 570 006, India
  • Communicated by Adam Paweł Wojda.
  • Received: 2017-03-03.
  • Accepted: 2017-06-14.
  • Published online: 2017-11-13.
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Cite this article as:
Chandrashekar Adiga, B. R. Rakshith, Upper bounds for the extended energy of graphs and some extended equienergetic graphs, Opuscula Math. 38, no. 1 (2018), 5-13, https://doi.org/10.7494/OpMath.2018.38.1.5

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