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.