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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.
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
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