Hamiltonicity in power graphs of a class of abelian groups

Abstract

The undirected power graph mathscr {G}(S) of a semigroup S is an undirected graph with vertex set S where two vertices u,vin S are adjacent if and only if there is a positive integer m such that u^{m}=v or v^{m}=u. Here, we investigate the power graphs of a class of abelian groups and answer, in this case, the question whether or not the power graph is Hamiltonian.