zbMATH — the first resource for mathematics

Domination numbers on the Boolean function graph of a graph. (English) Zbl 1110.05078
Summary: 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 $$B(G, L(G), \text{NINC})$$ of $$G$$ is a graph with vertex set $$V(G)\cup E(G)$$ and two vertices in $$B(G, L(G), \text{NINC} )$$ 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, cycle, point-set, restrained, split and non-split domination numbers of $$B_{1}(G)$$ and obtain bounds for the above numbers.
MSC:
 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
Full Text: