research-article

The property of edge-disjoint Hamiltonian cycles in transposition networks and hypercube-like networks

Discrete Applied Mathematics, Volume 181, Issue C

Pages 109 - 122

https://doi.org/10.1016/j.dam.2014.09.006

Published: 30 January 2015 Publication History

Abstract

The presence of 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 network. Edge-disjoint Hamiltonian cycles also provide the edge-fault tolerant hamiltonicity of an interconnection network. In this paper, we first study the property of edge-disjoint Hamiltonian cycles in transposition networks which form a subclass of Cayley graphs. The transposition networks include other famous network topologies as their subgraphs, such as meshes, hypercubes, star graphs, and bubble-sort graphs. We first give a novel decomposition of transposition networks. Using the proposed decomposition, we show that n -dimensional transposition network with n 5 contains four edge-disjoint Hamiltonian cycles. By using the similar approach, we present a linear time algorithm to construct two edge-disjoint Hamiltonian cycles on crossed cubes which is a variation of hypercubes. The proposed approach can be easily applied to construct two edge-disjoint Hamiltonian cycles on the other variations of hypercubes.

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Cited By

Zhang HWang YFan JHan YCheng B(2024)Constructing edge-disjoint spanning trees in several cube-based networks with applications to edge fault-tolerant communicationThe Journal of Supercomputing10.1007/s11227-023-05546-z80:2(1907-1934)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s11227-023-05546-z
Zhao YLi XMa M(2022)Embedded connectivity of some BC networksThe Journal of Supercomputing10.1007/s11227-022-04522-378:14(16605-16618)Online publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1007/s11227-022-04522-3
Pai K(2021)Embedding Three Edge-Disjoint Hamiltonian Cycles into Locally Twisted CubesComputing and Combinatorics10.1007/978-3-030-89543-3_31(367-374)Online publication date: 24-Oct-2021
https://dl.acm.org/doi/10.1007/978-3-030-89543-3_31
Show More Cited By

The property of edge-disjoint Hamiltonian cycles in transposition networks and hypercube-like networks
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis

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Published In

cover image Discrete Applied Mathematics

Discrete Applied Mathematics Volume 181, Issue C

January 2015

317 pages

ISSN:0166-218X

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Copyright © Elsevier B.V.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 30 January 2015

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Cited By

Zhang HWang YFan JHan YCheng B(2024)Constructing edge-disjoint spanning trees in several cube-based networks with applications to edge fault-tolerant communicationThe Journal of Supercomputing10.1007/s11227-023-05546-z80:2(1907-1934)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s11227-023-05546-z
Zhao YLi XMa M(2022)Embedded connectivity of some BC networksThe Journal of Supercomputing10.1007/s11227-022-04522-378:14(16605-16618)Online publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1007/s11227-022-04522-3
Pai K(2021)Embedding Three Edge-Disjoint Hamiltonian Cycles into Locally Twisted CubesComputing and Combinatorics10.1007/978-3-030-89543-3_31(367-374)Online publication date: 24-Oct-2021
https://dl.acm.org/doi/10.1007/978-3-030-89543-3_31
Pai K(2020)A Parallel Algorithm for Constructing Two Edge-Disjoint Hamiltonian Cycles in Crossed CubesAlgorithmic Aspects in Information and Management10.1007/978-3-030-57602-8_40(448-455)Online publication date: 10-Aug-2020
https://dl.acm.org/doi/10.1007/978-3-030-57602-8_40
Tu JZhou YSu G(2017)A kind of conditional connectivity of Cayley graphs generated by wheel graphsApplied Mathematics and Computation10.1016/j.amc.2016.12.015301:C(177-186)Online publication date: 15-May-2017
https://dl.acm.org/doi/10.1016/j.amc.2016.12.015

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