• X-DOMATIC PARTITION OF GRAPH VV(G) AND CHROMATIC NUMBER OF G

Abstract

Let be a bipartite graph. A X- domatic partition of is a partition of , all of whose classes are X-dominating set in . The X-domatic number of is the maximum number of classes of X-domatic partition of . The X-domatic number of is denoted by

Let G be a simple undirected graph. We obtain a sharp upper bound for the sum of chromatic number of G and X-domatic number of the bipartite graph obtained from G and characterize the corresponding extremal graphs.