An Embedding of Multiple Edge-Disjoint Hamiltonian Cycles on Enhanced Pyramid Graphs

The enhanced pyramid graph was recently proposed as an interconnection network model in parallel processing for maximizing regularity in pyramid networks. We prove that there are two edge-disjoint Hamiltonian cycles in the enhanced pyramid networks. This investigation demonstrates its superior property in edge fault tolerance. This result is optimal in the sense that the minimum degree of the graph is only four. Keywords—Enhanced Pyramid Model, Hamiltonian Cycle, Edge-Disjoint Cycle