Geodesic
Power graph of finite abelian groups
Algebra and discrete mathematics, Tome 16 (2013) no. 1, pp. 33-41.

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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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T. Tamizh Chelvam; M. Sattanathan. Power graph of finite abelian groups. Algebra and discrete mathematics, Tome 16 (2013) no. 1, pp. 33-41. http://geodesic.mathdoc.fr/item/ADM_2013_16_1_a4/

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