TY  - JOUR
ID  - Krzywkowski2012
LB  - Krzywkowski2012
AU  - Krzywkowski, Marcin
TI  - An upper bound on the total outer-independent domination number of a tree
ST  - An upper bound on the total outer-independent domination number of a tree
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 1
SP  - 153
EP  - 158
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.1.153
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.1.153
AB  - A total outer-independent dominating set of a graph \(G=(V(G),E(G))\) is a set \(D\) of vertices of \(G\) such that every vertex of \(G\) has a neighbor in \(D\), and the set \(V(G) \setminus D\) is independent. The total outer-independent domination number of a graph \(G\), denoted by \(\gamma_t^{oi}(G)\), is the minimum cardinality of a total outer-independent dominating set of \(G\). We prove that for every tree \(T\) of order \(n \geq 4\), with \(l\) leaves and \(s\) support vertices we have \(\gamma_t^{oi}(T) \leq (2n + s - l)/3\), and we characterize the trees attaining this upper bound.
KW  - total outer-independent domination
KW  - total domination
KW  - tree
SN  - 1232-9274
ER  -