Hamiltonian decomposition of the Cayley graph on the dihedral group $D_{2p}$ where $p$ is a prime

TL;DR

This paper presents a Hamiltonian decomposition of the Cayley graph on the dihedral group D_{2p} for prime p, contributing to the understanding of Hamiltonian cycles in algebraic graph structures.

Contribution

It provides the first explicit Hamiltonian decomposition for Cayley graphs on dihedral groups of order 2p with p prime.

Findings

Explicit Hamiltonian decompositions are constructed for these graphs.

The results extend known cases of Hamiltonian decompositions in algebraic graphs.

Abstract

In this note, we give the Hamiltonian decomposition of the Cayley graph on the dihedral group $D_{2p}$ where $p$ is a prime.