DOMINATION NUMBERS ON THE COMPLEMENT OF THE BOOLEAN FUNCTION GRAPH OF A GRAPH

For any graph G, let V(G) and E(G) denote the vertex set and the edge set of G respectively. The Boolean function graph B(G, L(G), NINC) of G is a graph with vertex set V (G) boolean OR E(G) and two vertices in B(G, L(G), NINC) are adjacent if and only if they correspond to two adjacent vertices of G, two adjacent edges of G or to a vertex and an edge not incident to it in G. For brevity, this graph is denoted by B-1(G). In this paper, we determine domination number, independent, connected, total, point-set, restrained, split and non-split domination numbers in the complement (B-1) over bar (G) of B-1(G) and obtain bounds for the above numbers.