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Algebra and Discrete Mathematics, 2013, Volume 16, Issue 1, Pages 33–41
(Mi adm432)
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This article is cited in 16 scientific papers (total in 16 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.
Received: 27.10.2011 Revised: 15.07.2012
Citation:
T. Tamizh Chelvam, M. Sattanathan, “Power graph of finite abelian groups”, Algebra Discrete Math., 16:1 (2013), 33–41
Linking options:
https://www.mathnet.ru/eng/adm432 https://www.mathnet.ru/eng/adm/v16/i1/p33
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