Disjoint paths of bounded length in large generalized cycles Original Research Article

A generalized p-cycle is a digraph whose set of vertices is partitioned in p parts that can be ordered in such a way that a vertex is adjacent only to vertices in the next part. The families of BGC(p,d,dp) and KGC(p,d,dp · k + dp) are the largest known p-cycles for their degree and diameter. In this paper we present a lower bound for the fault-diameter of a generalized cycle. Then we calculate the wide-diameter and the fault-diameter of the families mentioned above, by constructing disjoint paths between any pair of vertices. We conclude that the values of these parameters for BGC(p,d,dp) and KGC(p,d,dp+k + dp) exceed the lower bound at most in one unit.