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

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 FLTQ n ), and folded crossed cubes (denoted as FCQ n ) 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 FLTQ 5 and FCQ 5 , respectively. (2) According to the recursive structure of FLTQ n and FCQ n , there are three EDHCs in FLTQ n and FCQ n while n ≥ 6. (3) Considering that multiple faulty edges will occur randomly, the data broadcast performance of three EDHCs in FLTQ n and FCQ n is evaluated by simulation when 5 ≤ n ≤ 9.