@Article{Chaluvaraju2012,
author = "Chaluvaraju, B. and Vidya, K. A.",
title = "Bounds on perfect k-domination in trees: an algorithmic approach",
journal = "Opuscula Math.",
year = "2012",
volume = "32",
number = "4",
pages = "707--714",
doi = "http://dx.doi.org/10.7494/OpMath.2012.32.4.707",
url = "http://dx.doi.org/10.7494/OpMath.2012.32.4.707",
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",
issn = "1232-9274"
}