A two-colored digraph is a digraph each of whose arcs is colored by red or blue. An (h, k)-
walk in a two-colored digraph is a walk consisting of h red arcs and k blue arcs. A two-
colored digraph is primitive provided that for each pair of vertices u and ν there exists an (h,
k)-walk from u to ν and from ν to u. The smallest of such positive integer h+ k is called the
exponent of D. Let D be a primitive two colored digraph and let ν be a vertex in D. The local
exponent of D at the vertex ν, denoted exp (ν, D), is defined to be the smallest positive …