@Article{Atapour2012,
author = "Atapour, M. and Sheikholeslami, S. M. and Khodkar, Abdollah",
title = "Trees whose 2-domination subdivision number is 2",
journal = "Opuscula Math.",
year = "2012",
volume = "32",
number = "3",
pages = "423--437",
doi = "http://dx.doi.org/10.7494/OpMath.2012.32.3.423",
url = "http://dx.doi.org/10.7494/OpMath.2012.32.3.423",
abstract = "A set \(S\) of vertices in a graph \(G = (V,E)\) is a \(2\)-dominating set if every vertex of \(V\setminus S\) is adjacent to at least two vertices of \(S\). The \(2\)-domination number of a graph \(G\), denoted by \(\gamma_2(G)\), is the minimum size of a \(2\)-dominating set of \(G\). The \(2\)-domination subdivision number \(sd_{\gamma_2}(G)\) is the minimum number of edges that must be subdivided (each edge in \(G\) can be subdivided at most once) in order to increase the \(2\)-domination number. The authors have recently proved that for any tree \(T\) of order at least \(3\), \(1 \leq sd_{\gamma_2}(T)\leq 2\). In this paper we provide a constructive characterization of the trees whose \(2\)-domination subdivision number is \(2\).",
keywords = "\(2\)-dominating set, \(2\)-domination number, \(2\)-domination subdivision number",
issn = "1232-9274"
}