Opuscula Mathematica
Opuscula Math. 32, no. 4 (), 707-714
http://dx.doi.org/10.7494/OpMath.2012.32.4.707
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
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.