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### THE EXPONENT SET OF COMPLETE ASYMMETRIC 2-DIGRAPHS

#### Abstract

A 2-digraph is a digraph whose each ofits arcs is colored by either red

or blue. The exponent ofa 2-digraphD is the smallest positive integer

h + k over all possible nonnegative integers h and k such that for each

pair of vertices u and v in D there is a walk from u to v consisting of h

red arcs and k blue arcs. In this paper, we show that for n > 5 the

exponent set of complete asymmetic 2-digraphs on n vertices is Eo :

{2,3,4}.

Keywords: 2-digraphs, primitive, exponent.

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