Geodesic
Domination numbers on the Boolean function graph of a graph
Mathematica Bohemica, Tome 130 (2005) no. 2, pp. 135-151

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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 $B(G, L(G), \mathop {\mathrm NINC})$ of $G$ is a graph with vertex set $V(G)\cup E(G)$ and two vertices in $B(G, L(G), \mathop {\mathrm NINC})$ 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.
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 $B(G, L(G), \mathop {\mathrm NINC})$ of $G$ is a graph with vertex set $V(G)\cup E(G)$ and two vertices in $B(G, L(G), \mathop {\mathrm NINC})$ 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.
DOI : 10.21136/MB.2005.134129
Classification : 05C15, 05C45, 05C69, 06E30
Keywords: domination number; point-set domination number; split domination number; Boolean function graph 
Janakiraman, T. N.; Muthammai, S.; Bhanumathi, M. Domination numbers on the Boolean function graph of a graph. Mathematica Bohemica, Tome 130 (2005) no. 2, pp. 135-151. doi: 10.21136/MB.2005.134129
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