TY  - JOUR
ID  - Atapour2012
LB  - Atapour2012
AU  - Atapour, M.
AU  - Sheikholeslami, S. M.
AU  - Khodkar, Abdollah
TI  - Trees whose 2-domination subdivision number is 2
ST  - Trees whose 2-domination subdivision number is 2
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 3
SP  - 423
EP  - 437
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.3.423
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.3.423
AB  - 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 \(2\).
KW  - \(2\)-dominating set
KW  - \(2\)-domination number
KW  - \(2\)-domination subdivision number
SN  - 1232-9274
ER  -