Three Edge-Disjoint Hamiltonian Cycles in Folded Locally Twisted Cubes and Folded Crossed Cubes with Applications to All-to-All Broadcasting

Author:

Pai Kung-Jui1ORCID

Affiliation:

1. Department of Industrial Engineering and Management, Ming Chi University of Technology, New Taipei City 24301, Taiwan

Abstract

All-to-all broadcasting means to distribute the exclusive message of each node in the network to all other nodes. It can be handled by rings, and a Hamiltonian cycle is a ring that visits each vertex exactly once. Multiple edge-disjoint Hamiltonian cycles, abbreviated as EDHCs, have two application advantages: (1) parallel data broadcast and (2) edge fault-tolerance in network communications. There are three edge-disjoint Hamiltonian cycles on n-dimensional locally twisted cubes and n-dimensional crossed cubes while n ≥ 6, respectively. Locally twisted cubes, crossed cubes, folded locally twisted cubes (denoted as FLTQn), and folded crossed cubes (denoted as FCQn) are among the hypercube-variant network. The topology of hypercube-variant network has more wealth than normal hypercubes in network properties. Then, the following results are presented in this paper: (1) Using the technique of edge exchange, three EDHCs are constructed in FLTQ5 and FCQ5, respectively. (2) According to the recursive structure of FLTQn and FCQn, there are three EDHCs in FLTQn and FCQn while n ≥ 6. (3) Considering that multiple faulty edges will occur randomly, the data broadcast performance of three EDHCs in FLTQn and FCQn is evaluated by simulation when 5 ≤ n ≤ 9.

Funder

MOST through the Ministry of Science and Technology, Taiwan

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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