On the exponents of primitive, ministrong digraphs with shortest elementary circuit length s Original Research Article

Let MDs(n) = {D D is a primitive ministrong digraph with n vertices, and the shortest cycle length of D is s}, and bs(n) = max{γ(D) D set membership, variant MDs(n)}, where γ(D) is the primitive exponent of D. Our main results are: (1) we give explicit expressions for bs(n); (2) for s ≠ 2, 6, we give a necessary and sufficient condition for a digraph D set membership, variant MDs(n) with γ(D) = bs(n).