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2018 | Vol. 38, no. 1 | 5--13
Tytuł artykułu

For the extended energy of graphs and some extended equienergetic graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 [formula] 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 ≥ 9 starting with a pair of equienergetic regular graphs on 9 vertices.
Wydawca

Rocznik
Strony
5--13
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
  • University of Mysore, Manasagangothri Department of Studies in Mathematics Mysuru - 570 006, India, c_adiga@hotmail. com
  • University of Mysore, Manasagangothri Department of Studies in Mathematics Mysuru - 570 006, India, ranmsc08@yahoo. co.in
Bibliografia
  • [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. Stevanovic, 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. Cvetkovic, 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.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.baztech-23114596-9843-4ea9-9c4e-28d6f5ce43a4
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