Opuscula Math. 24, no. 2 (2004), 197-202

Opuscula Mathematica

# The minimum exponent of the primitive digraphs on the given number of arcs

Jolanta Rosiak

Abstract. Primitive digraphs on $$n$$ vertices, $$k$$ arcs and girth $$s$$ are considered. By $$a(n,k,s)$$ we mean the minimum exponent taken over all such digraphs. We estimate the number $$a(n,k,s)$$ using the Frobenius number for special values of $$k$$ and $$s$$.

Keywords: primitive directed graph, exponent, Frobenius number.

Mathematics Subject Classification: 05C20, 11A25.

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• Jolanta Rosiak
• Technical University of Szczecin, Institute of Mathematics, ul. Aleja Piastów 48/49, 70-310 Szczecin, Poland