Analysis of the relationship among the graphs isomorphic to multilayered cyclic fence graphs (MLCFG)

Multilayered cyclic fence graphs (MLCFG, E(m,n), F(m,n), D(m,n), G(m,n), X(m,n)) are proposed to be defined, all of which are composed of m 2n-membered cycles with periodic bridging. They are also cubic and bipartite. Hamiltonian wheel graph, H (n,[j(k)]), and parallelogram-shaped polyhex graph are also defined. All the members of MLCFGs are found to be isomorphic to the so-called "torus benzenoid graphs", while some members of MLCFGs are found to be related to the Hamilton wheel graphs. Through the construction of Hamilton wheel graph and the matrix representation by Kirby, a number of isomorphic relations among MLCFGs, Hamilton wheel graphs, and polyhex graphs were obtained. These relations among the MLCFG members were found also by the help of the characteristic quantities of MLCFGs.