Conditional Edge-Fault Hamiltonicity of Matching Composition Networks
A graph G is called Hamiltonian if there is a Hamiltonian cycle in G. The conditional edge- fault Hamiltonicity of a Hamiltonian graph G is the largest k such that after removing k faulty edges from G, provided that each node is incident to at least two fault-free edges, the resulting graph contains a Hamiltonian cycle. In this paper, we sketch common properties of a class of networks, called Matching Composition Networks (MCNs), such that the conditional edge- fault Hamiltonicity of MCNs can be determined from the obtained properties. We then apply our technical theorems to determine conditional edge- fault Hamiltonicities of several multiprocessor systems, including n-dimensional crossed cubes, n-dimensional twisted cubes, n-dimensional locally twisted cubes, n-dimensional generalized twisted cubes, and n-dimensional hyper Petersen networks. Moreover, we also demonstrate that our technical theorems can be applied to network construction.
hamiltonicity matching composition networks hamiltonian cycles multiprocessor systems algorithmic aspect of network problems conditional edge faults fault-tolerance graph theory restricted hypercube-like networks