Spider web networks: a family of optimal, fault tolerant, hamiltonian bipartite graphs

In this paper, we propose a honeycomb mesh variation, called a spider web network. Assume that m and n are positive even integers with mP 4. A spider web network SWðm; nÞ is a 3-regular bipartite planar graph with bipartition C and D. We prove that the honeycomb rectangular mesh HREMðm; nÞ is a spanning subgraph of SWðm; nÞ. We also prove that SWðm; nÞ e is hamiltonian for any e 2 E and SWðm; nÞ fc; dg remains hamiltonian for any c 2 C and d 2 D. These hamiltonian properties are optimal. 2003 Elsevier Inc. All rights reserved.