Global domination and neighborhood numbers in Boolean function graph of a graph

Abstract: 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 $V(G)\cup E(G)$ 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 $G$. In this paper, global domination number, total global domination number, global point-set domination number and neighborhood number for this graph are obtained.

Keywords: Boolean function graph, global domination number, neighborhood number

Classification (MSC2000): 05C15

Full text of the article:

• Compressed PostScript file (144 kilobytes)
• PDF file (148 kilobytes)