On irredundance coloring and irredundance compelling coloring of graphs

An irredundance coloring of a graph G is a proper coloring admitting a maximal irredundant set all of whose vertices receive different colors. The minimum number of colors required for an irredundance coloring of G is called the irredundance chromatic number of G, and is denoted by χ_i(G). An irredundance compelling coloring of G is a proper coloring of G in which every rainbow committee (a set consisting of one vertex of each color) is an irredundant set of G. The maximum number of colors required for an irredundance compelling coloring of G is called the irredundance compelling chromatic number of G, and is denoted by χ_irc(G). We make a detailed study of χ_i(G), χ_irc(G), derive bounds on these parameters and characterize extremal graphs attaining the bounds.