Ring embedding in faulty honeycomb rectangular torus

Hamilton paths in Cayley graphs on generalized dihedral groups

“…A family of trivalent vertex-transitive graphs that have garnered attention over the last thirty-five years have been called brick products in [1,2,5], honeycomb tori in [8,9,12,13,14,15], honeycomb toroidal graphs in [3], and hexagonal toroidal embeddings in [6,11]. Altshuler [6] studied them when he was considering Hamilton cycles in graphs embedded in the torus.…”

The globally Bi-3∗-connected property of the honeycomb rectangular torus

“…A graph G is hamiltonian if there exists a hamiltonian cycle in G. The hamiltonian properties are important aspects of designing an interconnection network. Many related works have appeared in the literature [3,6,8,12,13].…”

“…There are many studies on the properties of the honeycomb rectangular torus [3,8,11]. Stojmenovic [11] showed that the network cost of the honeycomb rectangular torus, which is defined as the product of degree and the diameter, is better than the other families based on mesh-connected computers and tori.…”

Generalized honeycomb torus is Hamiltonian

“…Stojmenovic [9] proposed three classes of honeycomb torus architectures: honeycomb hexagonal torus, honeycomb rectangular torus, and honeycomb parallelogramic torus. Due to lower node degree and lower implementation cost than those of a standard torus of the same size, these architectures have incurred great research interest [1,2,5,6,[8][9][10][11]. Cho and Hsu [3] found that all these honeycomb torus networks can be characterized in a unified way, and thereby proposed a class of interconnection networks known as the generalized honeycomb torus.…”

“…Megson et al [5,6] proved that hon-eycomb hexagonal torus is Hamiltonian, even in the presence of node failures. Cho and Hsu [2] discovered a Hamiltonian cycle for faulty honeycomb rectangular torus. As for generalized honeycomb torus, Cho and Hsu [3], and Yang and Megson [12] proved the existence of Hamiltonian cycles for some special cases.…”