MORE ON THE GLOBAL DOMINATOR CHROMATIC NUMBER

For a graph G = (V,E) and a vertex subset DCV, a vertex v Є V is called a dominator of D if v is adjacent to every vertex in D, and an anti-dominator of D if v is not adjacent to any vertex in D. Given a coloring C = {V۱, V۲, ...Vk} of G, a color class V₁ is a dominating color class or an anti-dominating color class for a vertex v if v dominates all vertices in V¿ or none, respectively. A coloring C is a global dominator coloring if each vertex in G has both a dominating and an anti-dominating color class. The global dominator chromatic number, denoted by Xgd (G), is the minimum number of colors required for a global dominator coloring of G. In this paper, we obtain more results on Xgd (G).

کلیدواژه ها:

global domination ، global dominator coloring ، cactus