A 6-Regular Torus Graph Family with Applications to Cellular and Interconnection Networks
Mihaela Iridon, David W. Matula · Journal of Graph Algorithms and Applications · 2002
This paper introduces a special graph family, together with an extensive characterization of some of its properties and two of its immediate applications. The graph denoted by Ti,j, is a regular hexavalent toroidal graph. The topological features of Ti,j include vertex symmetry, Hamiltonian decomposition, translation and rotation isomorphism. Topologically, the graph is a torus, while algebraically, it can also be expressed as a Cayley graph, defined on the cyclic group , where k can be determined from the (i,j) parameters defining graph Ti,j. As a direct consequence, the proposed graph, which has 2 2 2 ρ i, j = i + i ⋅j + j = ( i + j) −i