The -connected property of pyramid networks

Abstract: A -container of a graph is a set of -disjoint paths joining to . A -container of is a -container if it contains all the vertices of . A graph is -connected if there exists a -container between any two distinct vertices in . Let be the connectivity of . A graph is superconnected if is -connected for all . The pyramid network is one of the important networks applied in parallel and distributed computer systems. The connectivity of a pyramid network is three. In this paper, we prove that the pyramid network is -connected and superconnected for . [Copyright &y& Elsevier]