Dominator coloring of Kneser graph

Abstract

A dominator coloring (briefly DC) of a graph G is a proper coloring such that each vertex dominates every vertex of at least one color class (possibly its own class). The dominator chromatic number χd(G)  of G  is the smallest cardinality of color classes in a DC of G. By using Steiner triple systems, in this paper, we establish that the dominator coloring of the Kneser graph  KG(n, 2) is n for n ≥ 5.