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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2013, Volume 16, Issue 1, Pages 33–41 (Mi adm432)

RESEARCH ARTICLE

Power graph of finite abelian groups

T. Tamizh Chelvam, M. Sattanathan

Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India

Abstract: Let $G$ be a group. The power graph $\Gamma_P(G)$ of $G$ is a graph with vertex set $V(\Gamma_P(G)) = G$ and two distinct vertices $x$ and $y$ are adjacent in $\Gamma_P(G)$ if and only if either $x^i=y$ or $y^j=x$, where $2\leq i,j \leq n$. In this paper, we obtain some fundamental characterizations of the power graph. Also, we characterize certain classes of power graphs of finite abelian groups.

Keywords: power graph, planar graph, Eulerian graph, finite group.

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MSC: 05C25
Revised: 15.07.2012
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Citation: T. Tamizh Chelvam, M. Sattanathan, “Power graph of finite abelian groups”, Algebra Discrete Math., 16:1 (2013), 33–41

Citation in format AMSBIB
\Bibitem{CheSat13} \by T.~Tamizh~Chelvam, M.~Sattanathan \paper Power graph of finite abelian groups \jour Algebra Discrete Math. \yr 2013 \vol 16 \issue 1 \pages 33--41 \mathnet{http://mi.mathnet.ru/adm432} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184696} 

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

This publication is cited in the following articles:
1. Ma X., Feng M., “on the Chromatic Number of the Power Graph of a Finite Group”, Indag. Math.-New Ser., 26:4 (2015), 626–633
2. Feng M., Ma X., Wang K., “the Structure and Metric Dimension of the Power Graph of a Finite Group”, Eur. J. Comb., 43 (2015), 82–97
3. M. Feng, X. Ma, K. Wang, “The full automorphism group of the power (di)graph of a finite group”, Eur. J. Comb., 52:A (2016), 197–206
4. Z. Mehranian, A. Gholami, A. R. Ashrafi, “The spectra of power graphs of certain finite groups”, Linear Multilinear Algebra, 65:5 (2017), 1003–1010
5. A. K. Bhuniya, S. Bera, “Normal subgroup based power graphs of a finite group”, Commun. Algebr., 45:8 (2017), 3251–3259
6. N. Abd Rhani, Ali Nor Muhainiah Mohd, N. H. Sarmin, A. Erfanian, “On the dominating number, independent number and the regularity of the relative co-prime graph of a group”, Malays. J. Fundam. Appl. Sci., 13:2 (2017), 72–74
7. A. Hamzeh, “Signless and normalized Laplacian spectrums of the power graph and its supergraphs of certain finite groups”, J. Indones. Math. Soc., 24:1 (2018), 61–69
8. X. Ma, R. Fu, X. Lu, “On the independence number of the power graph of a finite group”, Indag. Math.-New Ser., 29:2 (2018), 794–806
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