Hamiltonicity in power graphs of a class of abelian groups

Abstract

AbstractThe undirected power graph $$\mathscr {G}(S)$$ G ( S ) of a semigroup S is an undirected graph with vertex set S where two vertices $$u,v\in S$$ u , v ∈ S are adjacent if and only if there is a positive integer m such that $$u^{m}=v$$ u m = v or $$v^{m}=u$$ 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.