Characterization Of Strong And Weak Dominating 2661539- Color Number In A Graph

Abstract Strong dominating 2661539- color number of a graph G is defined as the maximum number of color classes which are strong dominating sets of G and is denoted by sd2661539 G. Similarly weak dominating 2661539- color number of a graph G is defined as the maximum number of color classes which are weak dominating sets of G and is denoted by wd2661539 G. In both the cases the maximum is taken over all 2661539-coloring of G. In this paper some bounds for sd2661539 G and wd2661539 G are obtained and characterized the graphs for which strong dominating 2661539- color number and strong dominating 2661539- color number exist. Finally Nordhaus-Gaddum inequalities for sd2661539 G and wd2661539 G is derived.