• COMPLEMENTARY TREE DOMINATION IN BOOLEAN FUNCTION GRAPH B(Kp, INC,Kq) OF A GRAPH

Abstract

For any graph G, let V(G) and E(G) denote the vertex set and edge set of G respectively. The Boolean function graph B(K_p, INC,`K<sub>q</sub>) of G is a graph with vertex set V(G)ÈE(G) and two vertices  in B(K<sub>p</sub>, INC,`K_q) are adjacent if and only if they correspond to two adjacent vertices of G, two nonadjacent vertices of G or to a vertex and an edge incident to it in G. For brevity, this graph is denoted by B₄(G). In this paper, bounds of complementary tree domination number of Boolean function graph B₄(G) are obtained and this number is found for Boolean function graphs of particular graphs. Also a characterization of graphs for which tree domination number is equal to 2 is obtained.