Achromatic number of some classes of digraphs

Abstract

Let [Formula: see text] be a directed graph with [Formula: see text] vertices and [Formula: see text] arcs. A function [Formula: see text] where [Formula: see text] is called a complete coloring of [Formula: see text] if and only if for every arc [Formula: see text] of [Formula: see text], the ordered pair [Formula: see text] appears at least once. If the pair [Formula: see text] is not assigned, then [Formula: see text] is called a [Formula: see text] [Formula: see text] [Formula: see text] of [Formula: see text]. The maximum [Formula: see text] for which [Formula: see text] admits a proper complete coloring is called the [Formula: see text] [Formula: see text] of [Formula: see text] and is denoted by [Formula: see text]. We obtain the upper bound for the achromatic number of digraphs and regular digraphs and investigate the same for some classes of digraphs such as unipath, unicycle, circulant digraphs, etc.