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Submitted
April 4, 2017
Accepted
June 11, 2017
Published
January 21, 2018
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Abstract

‎The aim of this article is to compute the signless and normalized Laplacian spectrums of the power graph‎, ‎its main supergraph and cyclic graph of dihedral and dicyclic groups‎.

Keywords

Power graph‎ ‎signless Laplacian‎ ‎normalized Laplacian‎ ‎cyclic graph‎ ‎main supergraph‎ .

Article Details

How to Cite
Hamzeh, A. (2018). Signless and normalized Laplacian spectrums of the power graph and its supergraphs of certain finite groups. Journal of the Indonesian Mathematical Society, 24(1), 61–69. https://doi.org/10.22342/jims.24.1.478.61-69
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References

  1. P. J. Cameron and S. Ghosh, The power graph of a finite group, Discrete Math. 311 (2011)
  2. -1222.
  3. P.J. Cameron, The power graph of a finite group, II, J. Group Theory 13 (2010) 779-783.
  4. S. Chattopadhyaya and P. Panigrahi, On Laplacian spectrum of power graphs of finite cyclic and
  5. dihedral groups, Linear Multilinear Algebra 63(7) (2015) 1345-1355.
  6. A. Hamzeh and A. R. Ashrafi, The main supergraph of the power graph of a finite group, submitted.
  7. A. Hamzeh and A. R. Ashrafi, Automorphism group of supergraphs of the power graph of a finite
  8. group, European J. Combin., 60 (2017) 82-88.
  9. A. Hamzeh, Spectrum and L-spectrum of the cyclic group, Southeast Asian Bull. Math., accepted.
  10. A. Hamzeh and A. R. Ashrafi, Spectrum and L-spectrum of the power graph and its main
  11. supergraph for certain finite groups, submitted.
  12. A. Kelarev, J. Ryan and J. Yearwood, Cayley graphs as classifiers for data mining: The in uence
  13. of asymmetries, Discrete Math. 309(17)(2009) 5360-5369.
  14. A.V. Kelarev and S.J. Quinn, A combinatorial property and power graphs of semigroups, Com-
  15. ment. Math. Univ. Carolin. 45 (1) (2004) 1-7.
  16. A.V. Kelarev, Graph Algebras and Automata, Marcel Dekker, New York, 2003.
  17. A.V. Kelarev and S.J. Quinn, Directed graphs and combinatorial properties of semigroups, J.
  18. Algebra 251 (1) (2002) 16-26.
  20. A.V. Kelarev, S.J. Quinn and R. Smoliikova, Power graphs and semigroups of matrices, Bull.
  21. Austral. Math. Soc. 63 (2) (2001) 341-344.
  22. A.V. Kelarev and S.J. Quinn, A combinatorial property and power graphs of groups, Contribu-
  23. tions to General Algebra 12 (Vienna, 1999), 229-235, Heyn, Klagenfurt, 2000.
  24. X.L. Ma, H.Q. Wei and Guo Zhong, The cyclic graph of a finite group, Algebra 2013 (2013)
  25. Article ID 107265, 1-7.
  26. Z. Mehranian, A. Gholami and A.R. Ashrafi, The Spectra of power graphs of certain finite groups,
  27. Linear Multilinear Algebra, 65 (5) (2017) 1003-1010.
  28. J. S. Rose, A Course on Group Theory, Cambridge University Prees, Cambridge, New York-
  29. Melbourne, 1978.
  30. G. Sabidussi, Graph Derivatives, Math. Z. 76 (1961) 385-401.
  31. T. Tamizh Chelvam and M. Sattanathan, Power graph of finite abelian groups, Algebra Discrete
  32. Math. 16 (1) (2013) 33-41.
  33. D. B. West, Introduction to Graph Theory, Second Edition, Prentice Hall, Inc., Upper Saddle
  34. River, NJ, 2001.
  35. B-F. Wu, Y-Y. Lou and C-X. He, Signless Laplacian and normalized Laplacian on the
  36. H-join operation of graphs, Discrete Math. Algorithm. Appl. 06 (2014) [13 pages] DOI:
  37. http://dx.doi.org/10.1142/S1793830914500463.