On Hamiltonian cycles of power graphs of abelian groups

TL;DR

This paper investigates the existence of Hamiltonian cycles in the undirected power graphs of abelian groups, introducing a weighted Hamiltonian cycle concept and establishing general results.

Contribution

It introduces a weighted Hamiltonian cycle framework and provides new theoretical results on Hamiltonian cycles in power graphs of abelian groups.

Findings

Developed a weighted Hamiltonian cycle concept.

Proved general results on Hamiltonian cycles.

Analyzed conditions for Hamiltonicity in power graphs.

Abstract

In this article we discuss the question of presence of Hamiltonian cycle in the un-directed power graph of a group. In the process we develop weighted Hamiltonian cycle concept and prove a few general results regarding the Hamiltonian question.