Sriparna Chattopadhyay, Pratima Panigrahi, “Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups”, Algebra Discrete Math., 18:1 (2014), 42

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Algebra and Discrete Mathematics, 2014, Volume 18, Issue 1, Pages 42–49 (Mi adm480)

This article is cited in 16 scientific papers (total in 16 papers)

RESEARCH ARTICLE

Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups

Sriparna Chattopadhyay, Pratima Panigrahi

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

Full-text PDF (394 kB) Citations (16)

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Abstract: The power graph of a finite group is the graph whose vertices are the elements of the group and two distinct vertices are adjacent if and only if one is an integral power of the other. In this paper we discuss the planarity and vertex connectivity of the power graphs of finite cyclic, dihedral and dicyclic groups. Also we apply connectivity concept to prove that the power graphs of both dihedral and dicyclic groups are not Hamiltonian.

Keywords: power graph, connectivity, planarity, cyclic group, dihedral group, dicyclic group.

Received: 14.07.2012
Revised: 04.04.2013

Bibliographic databases:

Document Type: Article

MSC: 05C25, 05C10, 05C40

Language: English

Citation: Sriparna Chattopadhyay, Pratima Panigrahi, “Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups”, Algebra Discrete Math., 18:1 (2014), 42–49

Citation in format AMSBIB

\Bibitem{ChaPan14}

\by Sriparna~Chattopadhyay, Pratima~Panigrahi

\paper Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups

\jour Algebra Discrete Math.

\yr 2014

\vol 18

\issue 1

\pages 42--49

\mathnet{http://mi.mathnet.ru/adm480}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3280255}

Linking options:

https://www.mathnet.ru/eng/adm480

https://www.mathnet.ru/eng/adm/v18/i1/p42

This publication is cited in the following 16 articles:

Chattopadhyay S., Patra K.L., Sahoo B.K., “Minimal Cut-Sets in the Power Graphs of Certain Finite Non-Cyclic Groups”, Commun. Algebr., 49:3 (2021), 1195–1211
Kumar A., Selvaganesh L., Cameron P.J., Chelvam T.T., “Recent Developments on the Power Graph of Finite Groups - a Survey”, AKCE Int. J. Graphs Comb., 18:2 (2021), 65–94
Panda R.P., Patra K.L., Sahoo B.K., “On the Minimum Degree of the Power Graph of a Finite Cyclic Group”, J. Algebra. Appl., 20:3 (2021), 2150044
X. Y. Chen, A. R. Moghaddamfar, M. Zohourattar, “Some properties of various graphs associated with finite groups”, Algebra Discrete Math., 31:2 (2021), 195–211
Liu Y., Yuan J.-b., Dai W.-j., Li D., “Three-State Quantum Walk on the Cayley Graph of the Dihedral Group”, Quantum Inf. Process., 20:3 (2021), 106
Ali F., Fatima S., Wang W., “on the Power Graphs of Certain Finite Groups”, Linear Multilinear Algebra, 2020
S. Chattopadhyay, K. L. Patra, B. K. Sahoo, “Vertex connectivity of the power graph of a finite cyclic group II”, J. Algebra. Appl., 19:2 (2020), 2050040
K. Pourghobadi, S. H. Jafari, “The diameter of proper power graphs of alternating groups”, Util. Math., 113 (2019), 121–129
R. P. Panda, “Laplacian spectra of power graphs of certain finite groups”, Graphs Comb., 35:5 (2019), 1209–1223
S. Chattopadhyay, K. L. Patra, B. K. Sahoo, “Vertex connectivity of the power graph of a finite cyclic group”, Discret Appl. Math., 266:SI (2019), 259–271
R. P. Panda, K. V. Krishna, “On connectedness of power graphs of finite groups”, J. Algebra. Appl., 17:10 (2018), 1850184
S. Chattopadhyay, P. Panigrahi, F. Atik, “Spectral radius of power graphs on certain finite groups”, Indag. Math.-New Ser., 29:2 (2018), 730–737
R. P. Panda, K. V. Krishna, “On the minimum degree, edge-connectivity and connectivity of power graphs of finite groups”, Commun. Algebr., 46:7 (2018), 3182–3197
A. Doostabadi, M. Farrokhi D.G., “Embeddings of (proper) power graphs of finite groups”, Algebra Discrete Math., 24:2 (2017), 221–234
S. Chattopadhyay, P. Panigrahi, “Some structural properties of power graphs and k-power graphs of finite semigroups”, J. Discret. Math. Sci. Cryptogr., 20:5 (2017), 1101–1119
Chattopadhyay S., Panigrahi P., “on Laplacian Spectrum of Power Graphs of Finite Cyclic and Dihedral Groups”, Linear Multilinear Algebra, 63:7 (2015), 1345–1355

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	89

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