### Power graph of finite abelian groups

#### 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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