Restricted domination parameters in graphs

Wayne Goddard and Michael A. Henning
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Wayne Goddard: Clemson University
Michael A. Henning: University of KwaZulu-Natal

Journal of Combinatorial Optimization, 2007, vol. 13, issue 4, No 4, 353-363

Abstract: Abstract In a graph G, a vertex dominates itself and its neighbors. A subset S ⊂eqV(G) is an m-tuple dominating set if S dominates every vertex of G at least m times, and an m-dominating set if S dominates every vertex of G−S at least m times. The minimum cardinality of a dominating set is γ, of an m-dominating set is γ m , and of an m-tuple dominating set is mtupledom. For a property π of subsets of V(G), with associated parameter f_π, the k-restricted π-number r k (G,f_π) is the smallest integer r such that given any subset K of (at most) k vertices of G, there exists a π set containing K of (at most) cardinality r. We show that for 1

Keywords: Domination number; Double domination; k-domination; Restricted (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10878-006-9037-1

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