MATHEMATICA BOHEMICA, Vol. 130, No. 3, pp. 231-246 (2005)

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

T. N. Janakiraman, S. Muthammai, M. Bhanumathi

T. N. Janakiraman, National Institute of Technology, Tiruchirappalli 620 015, India, e-mail:; S. Muthammai, M. Bhanumathi, Government Arts College for Women, Pudukkottai 622 001, India

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

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