A graph G = (V,E) is said to be conditional k-edge-fault pancyclic if, after removing k faulty edges from G and provided that each node is incident to at least two fault-free edges, the resulting graph contains a cycle of every length from its girth to |V| inclusive. In this paper, we sketch the common properties of a class of networks called Matching Composition Networks (MCNs), such that the conditional edge-fault pancyclicity of MCNs can be determined from the derived properties. We then apply our technical theorem to show that an m-dimensional hyper-Petersen network is conditional (2m-5)-edge-fault pancyclic.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics