### Signless and normalized Laplacian spectrums of the power graph and its supergraphs of certain finite groups

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

P. J. Cameron and S. Ghosh, The power graph of a finite group, Discrete Math. 311 (2011)

-1222.

P.J. Cameron, The power graph of a finite group, II, J. Group Theory 13 (2010) 779-783.

S. Chattopadhyaya and P. Panigrahi, On Laplacian spectrum of power graphs of finite cyclic and

dihedral groups, Linear Multilinear Algebra 63(7) (2015) 1345-1355.

A. Hamzeh and A. R. Ashrafi, The main supergraph of the power graph of a finite group, submitted.

A. Hamzeh and A. R. Ashrafi, Automorphism group of supergraphs of the power graph of a finite

group, European J. Combin., 60 (2017) 82-88.

A. Hamzeh, Spectrum and L-spectrum of the cyclic group, Southeast Asian Bull. Math., accepted.

A. Hamzeh and A. R. Ashrafi, Spectrum and L-spectrum of the power graph and its main

supergraph for certain finite groups, submitted.

A. Kelarev, J. Ryan and J. Yearwood, Cayley graphs as classifiers for data mining: The in uence

of asymmetries, Discrete Math. 309(17)(2009) 5360-5369.

A.V. Kelarev and S.J. Quinn, A combinatorial property and power graphs of semigroups, Com-

ment. Math. Univ. Carolin. 45 (1) (2004) 1-7.

A.V. Kelarev, Graph Algebras and Automata, Marcel Dekker, New York, 2003.

A.V. Kelarev and S.J. Quinn, Directed graphs and combinatorial properties of semigroups, J.

Algebra 251 (1) (2002) 16-26.

A.V. Kelarev, S.J. Quinn and R. Smoliikova, Power graphs and semigroups of matrices, Bull.

Austral. Math. Soc. 63 (2) (2001) 341-344.

A.V. Kelarev and S.J. Quinn, A combinatorial property and power graphs of groups, Contribu-

tions to General Algebra 12 (Vienna, 1999), 229-235, Heyn, Klagenfurt, 2000.

X.L. Ma, H.Q. Wei and Guo Zhong, The cyclic graph of a finite group, Algebra 2013 (2013)

Article ID 107265, 1-7.

Z. Mehranian, A. Gholami and A.R. Ashrafi, The Spectra of power graphs of certain finite groups,

Linear Multilinear Algebra, 65 (5) (2017) 1003-1010.

J. S. Rose, A Course on Group Theory, Cambridge University Prees, Cambridge, New York-

Melbourne, 1978.

G. Sabidussi, Graph Derivatives, Math. Z. 76 (1961) 385-401.

T. Tamizh Chelvam and M. Sattanathan, Power graph of finite abelian groups, Algebra Discrete

Math. 16 (1) (2013) 33-41.

D. B. West, Introduction to Graph Theory, Second Edition, Prentice Hall, Inc., Upper Saddle

River, NJ, 2001.

B-F. Wu, Y-Y. Lou and C-X. He, Signless Laplacian and normalized Laplacian on the

H-join operation of graphs, Discrete Math. Algorithm. Appl. 06 (2014) [13 pages] DOI:

http://dx.doi.org/10.1142/S1793830914500463.

DOI: https://doi.org/10.22342/jims.24.1.478.%25p

### Refbacks

- There are currently no refbacks.

**Journal of the Indonesian Mathematical Society**

Mathematics Department, Universitas Gadjah Mada

Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243

Email: jims.indoms@gmail.com

p-ISSN: 2086-8952 | e-ISSN: 2460-0245

Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License