HIT NUMBER OF DIRECTED GRAPHS
Abstract
A total coloring f of a directed graph G is called edge-irregular if for any two edges e1=u1v1 and e2=u2v2 of G the associated ordered triples (f(u1), f(e1), f(v1)) and (f(u2), f(e2), f(v2)) are different. The problem is to determine the minimum number of colors used in such a coloring of G. This parameter of G is denoted by hit(G). In this paper we survey results for this parameter.
Keywords
directed graph; graph coloring; graph labeling
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