Honeycomb toroidal graphs are Cayley graphs

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.…”

“…Recently [3] it was shown that these trivalent graphs are Cayley graphs on generalized dihedral groups. In this paper we study Hamilton paths in the latter family of graphs.…”

Efficient domination in Cayley graphs of generalized dihedral groups

“…There is another reason why the investigation of cubic Cayley graphs of generalized dihedral groups is of interest. As was proved in [1] it turns out that this class of graphs contains all so-called honeycomb toroidal graphs (see Section 2 for the definition) which turn out to be useful in the theory of interconnection networks (see [1,7,11,12,20,22,25] and the references therein).…”

“…We now introduce a particular family of cubic graphs that will play one of the central roles in this paper. The graphs in question are known in the literature under various different names such as brick products, generalized honeycomb tori and honeycomb toroidal graphs (see for instance [1,7,11,12,20,22,25]). In this paper we stick to the name honeycomb toroidal graphs.…”

Target Set Selection Problem for Honeycomb Networks

“…Majority threshold model has many applications in distributed computing such as maintaining data consistency in a distributed system, fault-local mending in distributed network and overcoming failure in distributed computing [22,23,27,28]. On the other hand, honeycomb networks have been suggested as an attractive architecture for interconnected networks which have been widely investigated in parallel and distributed applications (see [3,30] and references therein). In this paper, we study target set selection problem under strict majority thresholds on different kinds of honeycomb networks such as honeycomb mesh HM t , honeycomb torus HT t , honeycomb rectangular torus HReT(m, n), honeycomb rhombic torus HRoT(m, n), generalized honeycomb rectangular torus GHT(m, n), planar hexagonal grid PHG(m, n), cylindrical hexagonal grid CHG(m, n), and toroidal hexagonal grid THG(m, n) (all terms will be defined in later sections).…”