Matching Preclusion for Enhanced Pyramid Networks

The matching preclusion number of a graph is the minimum number of edges whose deletion leaves the resulting graph that has neither perfect matchings nor almost perfect matchings. This concept was introduced as a measure of robustness in the event of edge failure in interconnection networks. The pyramid network is one of the important networks applied in parallel and distributed computer systems. Chen et al. in 2004 proposed a new hierarchy structure, called the enhanced pyramid network, by replacing each mesh in a pyramid network with a torus. An enhanced pyramid network of n layers is denoted by EPM(n). In this paper, we prove that the matching preclusion number of EPM(n) is 9 where n ≥ 4.