Bipartite theory on Neighbourhood dominating and global dominating sets of a graph

Bipartite theory of graphs was formulated by Stephen Hedetniemi and Renu Laskar in which concepts in Graph theory have equivalent formulations as concepts for bipartite graphs.  We give the bipartite version of Neighbourhood sets, Line neighbourhood set and Global dominating set

X− Dominating colour transversals in graphs

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