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

Abstract

In this paper, we propose a honeycomb mesh variation, called a spider web network. Assume that m and n are positive even integers with m⩾4. A spider web network SW( m, n) is a 3-regular bipartite planar graph with bipartition C and D. We prove that the honeycomb rectangular mesh HREM( m, n) is a spanning subgraph of SW( m, n). We also prove that SW( m, n)− e is hamiltonian for any e∈ E and SW( m, n)−{ c, d} remains hamiltonian for any c∈ C and d∈ D. These hamiltonian properties are optimal.