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2016 | 4 | 1 | 121-129
Tytuł artykułu

On some characterizations of strong power graphs of finite groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G be a finite group of order n. The strong power graph Ps(G) of G is the undirected graph whose vertices are the elements of G such that two distinct vertices a and b are adjacent if am1=bm2 for some positive integers m1, m2 < n. In this article we classify all groups G for which Ps(G) is a line graph. Spectrum and permanent of the Laplacian matrix of the strong power graph Ps(G) are found for any finite group G.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
Strony
121-129
Opis fizyczny
Daty
zaakceptowano
2015-01-22
otrzymano
2015-08-21
online
2016-02-05
Twórcy
  • Department of Mathematics, Visva-Bharati, Santiniketan-731235, India
autor
  • Department of Mathematics, Visva-Bharati, Santiniketan-731235, India
Bibliografia
  • [1] J. Abawajy, A. V. Kelarev and M. Chowdhury, Power graphs: A survey, Electron. J. Graph Theory Appl, 1(2013), 125-147.
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  • [12] Y. Hou, Unicyclic graphs with minimal energy, J. Math. Chem, 29(2001), 163-168. [Crossref]
  • [13] Y. Hou, Z. Teng and C. W. Woo, On the spectral radius, k degree and the upper bound of energy in a graph, MATCH Commun. Math. Comput. Chem., 57(2007), 341-350.
  • [14] T. W. Hungerford, Algebra, Graduate Text in Mathematics 73, Springer-Verlag, New York(NY), (1974).
  • [15] A. V. Kelarev and S. J. Quinn, A combinatorial property and power graphs of groups, Contributions to General Algebra, 12(Heyn, Klagenfurt, 2000), 229-235.
  • [16] X. Ma, On the spectra of strong power graphs of finite groups, Preprint arXiv:1506.07817 [math.GR]2015.
  • [17] H. Minc, Permanents, Addition-Wesley, Reading, Mass, 1978.
  • [18] H. Minc, Theory of permanents, Linear and Multilinear Algebra, 12(1983), 227-263.
  • [19] B. Mohar, The Laplacian spectrumof graphs, In: Y. Alavi, G. Chartrand, Oellermann OR, A. J. Schwenk, editors. Graph Theory, combinatorics, and aplications, Wiley, New York, 2(1991), 871-898.
  • [20] G. Singh and K. Manilal, Some generalities on power graphs and strong power graphs, Int. J. Contemp. Math Sciences, 5(55)(2010), 2723-2730.
  • [21] D. B. West, Introduction to Graph theory, 2nd ed., Pearson education, 2001.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2016-0012
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