Abstract: Let kbe a positive integer and let Gbe a k-connected graph or digraph. The k-Rabin number of
Gis the minimum lsuch that for every distinct
vertices there
exist kvertex-disjoint (except at x) paths of length at most lfrom xto Thereis a generalization of the k-Rabin number, called the strong
k-Rabin number in
which are
not necessarily distinct. We remark that In
this paper, we give an upper bound of strong k-Rabin numbers of k-connected
(di)graphs which satisfy a
condition. As applications, we get an upper bound of the strong Rabin number of
de Bruijn digraph Furthermore, this result can be used not only to
resolve some known strong Rabin numbers of (di)graphs but also to determine
unknown strong Rabin numbers of Kautz digraphand star network (nis odd).
