Recent Advancements in Graph Theory

26Total Global Dominator Coloring of Graphs

K.P. Chithra

Department of Mathematics,CHRIST (Deemed to be University),Bengaluru, Karnataka (INDIA)E-mail: [e-mail]

Mayamma Joseph

Department of Mathematics,CHRIST (Deemed to be University),Bengaluru, Karnataka (INDIA)

Let {V₁, V₂, V₃…, V_k} be the collection of color classes corresponding to a proper coloring c of a graph G = (V, E), where V_i represents the set of vertices with color c_i. A color class V_i is called a proper dom-color class of a vertex v ∈ V if v dominates every vertex in V_i and V_i ≠ {v}. A color class V_j is called an anti dom-color class of v if v does not dominate any of the vertices in V_j. The coloring c is called a total global dominator coloring of ...