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

This article is cited in 8 scientific papers (total in 8 papers)

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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Bibliographic databases:
MSC: 05C25
Received: 27.10.2011
Revised: 15.07.2012
Language:

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
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    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  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  zmath  isi  scopus
    5. A. K. Bhuniya, S. Bera, “Normal subgroup based power graphs of a finite group”, Commun. Algebr., 45:8 (2017), 3251–3259  crossref  mathscinet  zmath  isi  scopus
    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  mathscinet  isi
    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  mathscinet  isi
    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  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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