Power graph of finite abelian groups

T. Tamizh Chelvam, M. Sattanathan


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.


power graph, planar graph, Eulerian graph, finite group

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