Constructing Two Edge-Disjoint Hamiltonian Cycles in Locally Twisted Cubes

TL;DR

This paper demonstrates the construction of two edge-disjoint Hamiltonian cycles in the n-dimensional locally twisted cube, enhancing its utility for parallel algorithms and network reliability.

Contribution

It presents a method to construct two edge-disjoint Hamiltonian cycles in $LTQ_n$ for any $n \\geq 4$, a novel property for this network variant.

Findings

Two edge-disjoint Hamiltonian cycles exist in $LTQ_n$ for all $n \\geq 4$

The construction improves network robustness and load balancing

Enhances algorithm implementation in $LTQ_n$ networks

Abstract

The $n$-dimensional hypercube network $Q_n$ is one of the most popular interconnection networks since it has simple structure and is easy to implement. The $n$-dimensional locally twisted cube, denoted by $LTQ_n$, an important variation of the hypercube, has the same number of nodes and the same number of connections per node as $Q_n$. One advantage of $LTQ_n$ is that the diameter is only about half of the diameter of $Q_n$. Recently, some interesting properties of $LTQ_n$ were investigated. In this paper, we construct two edge-disjoint Hamiltonian cycles in the locally twisted cube $LTQ_n$, for any integer $n\geqslant 4$. The presence of two edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the locally twisted cube.