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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. [ABSTRACT FROM AUTHOR]

In IP networks, packet forwarding is destination-based and hop-by-hop, and routes are built as needed. Kwong et al. introduced a protection routing in which packet delivery to the destination node can proceed uninterrupted in the event of any single node or link failure. He then showed that "whether there is a protection routing to the destination" is NP-complete. Tapolcai found that two completely independent spanning trees, abbreviated as CISTs, can be used to configure the protection routing. In this paper, we proposed dual protection routing trees, denoted as dual-PRTs to replace CISTs, which are less restrictive than CISTs. Next, we proposed a transformation algorithm that uses dual-PRTs to configure the protection routing. Taking complete graphs Kn, complete bipartite graphs Km,n, hypercubes Qn, and locally twisted cubes LTQn as examples, we provided a recursive method to construct dual-PRTs on them. This article showed that there are no two CISTs on K3,3, Q3, and LTQ3, but there exist dual-PRTs that can be used to configure the protection routing. As shown in the performance evaluation of simulation results, for both Qn and LTQn, we get the average path length of protection routing configured by dual-PRTs is shorter than that by two CISTs. [ABSTRACT FROM AUTHOR]