Hamiltonian cycles of power graph of abelian groups

In this article we discuss the question of existence of Hamiltonian cycles in the undirected power graph of a group, where power graph is defined as a graph with the group as the vertex set and edges between two distinct elements whenever one is a power of the other. We describe a new structural description of power graphs through vertex weighted directed graphs. We develop the theory of weighted Hamiltonian paths in a weighted graph. We solve the Hamiltonian question completely for power graphs of a class of finite abelian groups, namely (ℤ_p)^n × (ℤ_q)^m where p , q are distinct primes.