Global dominator coloring of unicyclic graphs

Let S ? V. A vertex v ? V is a dominator of S if v dominates every vertex in S and v is said to be an anti-dominator of S if v dominates none of the vertices of S. Let C = (V-1, V-2,..., V-k) be a coloring of G and let v ? V (G). A color class V-i is called a dom-color class or an anti-dom-color class of the vertex v according as v is a dominator of V-i or an anti-dominator of V-i. The coloring C is called a global dominator coloring of G if every vertex of G has a dom-color class and an anti-dom-color class in C. The minimum number of colors required for a global dominator coloring of G is called the global dominator chromatic number and is denoted by ?(gd)(G). This parameter was introduced in [I. S. Hamid and M. Rajeswari, Global dominator coloring of graphs, Discuss. Math. Graph Theory 39 (2019) 325-339]. This paper further extends the study by obtaining the value of ?(gd) for unicyclic graphs.