Constructing Two Edge-Disjoint Hamiltonian Cycles in Locally Twisted Cubes

Details Constructing Two Edge-Disjoint Hamiltonian Cycles in Locally Twisted Cubes Constructing Two Edge-Disjoint Hamiltonian Cycles in Locally Twisted Cubes

2010-10-12

arxiv.org/abs/1010.2466v1

Computer Science

Distributed, Parallel, and Cluster Computing

7 pages, 4 figures

Scientific paper

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.

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