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The dual neighborhood number of a graph. (English) Zbl 1217.05176

Summary: A set \(S \subseteq V(G)\) is a neighborhood set of a graph \(G = (V, E)\), if \(G =\cup _{v\in S} [N(v)]\), where \([N(v)]\) is the sub graph of a graph \(G\) induced by \(v\) and all vertices adjacent to \(v\). The dual neighborhood number \(\eta +2(G) =\) Min. \(|S1| + |S2| : S1, S2\) are two disjoint neighborhood set of \(G\). In this paper, we extended the concept of neighborhood number to dual neighborhood number and its relationship with other neighborhood related parameters are explored.

MSC:

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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