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 & GE; 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 & GE; 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 & LE; n & LE; 9.