X− Dominating colour transversals in graphs

Abstract

Let G = (X, Y,E) be a bipartite graph. A X-dominating set D ⊆ X is called a X−dominating colour transversal set of a graph G if D is a transversal of at least one $chi$−partition of G.The minimum cardinal- ity of a X−dominating colour transversal set is called X−dominating colour transversal number and is denoted by $chi_{dct}(G)$. We find the bounds of X−dominating colour transversal number and characterize the graphs attaining the bound.

Keywords

• X−dominating set
• X−dominating colour transversal set
• X−chromatic partition