For the extended energy of graphs and some extended equienergetic graphs

• Autorzy: Adiga C. , Rakshith B. R.

Identyfikatory

DOI

10.7494/OpMath.2018.38.1.5

• 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.

Słowa kluczowe

EN

energy of a graph; extended energy of a graph; extended equienergetic graphs

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 1
• Strony: 5--13
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Adiga C.

• University of Mysore, Manasagangothri Department of Studies in Mathematics Mysuru - 570 006, India

autor

Rakshith B. R.

• University of Mysore, Manasagangothri Department of Studies in Mathematics Mysuru - 570 006, India

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.
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• [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.
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• [14] J. Liu, B. Liu, On a pair of equienergetic graphs, MATCH Commun. Math. Comput. Chem. 59 (2008), 275-278.
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• [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.
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• [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).