Opuscula Mathematica
Opuscula Math. 32, no. 4 (), 707-714
Opuscula Mathematica

Bounds on perfect k-domination in trees: an algorithmic approach

Abstract. Let \(k\) be a positive integer and \(G = (V;E)\) be a graph. A vertex subset \(D\) of a graph \(G\) is called a perfect \(k\)-dominating set of \(G\) if every vertex \(v\) of \(G\) not in \(D\) is adjacent to exactly \(k\) vertices of \(D\). The minimum cardinality of a perfect \(k\)-dominating set of \(G\) is the perfect \(k\)-domination number \(\gamma_{kp}(G)\). In this paper, a sharp bound for \(\gamma_{kp}(T)\) is obtained where \(T\) is a tree.
Keywords: \(k\)-domination, perfect domination, perfect \(k\)-domination.
Mathematics Subject Classification: 05C69, 05C70.
Cite this article as:
B. Chaluvaraju, K. A. Vidya, Bounds on perfect k-domination in trees: an algorithmic approach, Opuscula Math. 32, no. 4 (2012), 707-714, http://dx.doi.org/10.7494/OpMath.2012.32.4.707
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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