On cycles of directed graphs (Q1106238)

Let G be a directed graph, a any fixed vertex of G and b an arbitrary vertex of G. Suppose \(\lambda\) (b) is the number equal to the length of the shortest (simple) path from a to b. The author proves the following: Let G be a directed graph such that (1) the cycles of G have equal length k, (2) every pair of cycles of G has a vertex in common. Then there is an integer i (mod k) such that G has one and only one vertex satisfying \(\lambda (b)=i\).