TY  - JOUR
ID  - Lemańska2008
LB  - Lemańska2008
AU  - Lemańska, Magdalena
AU  - Patyk, Agnieszka
TI  - Weakly connected domination critical graphs
ST  - Weakly connected domination critical graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2008
VL  - 28
IS  - 3
SP  - 325
EP  - 330
DO  - http://dx.doi.org/10.7494/OpMath.2008.28.3.325
UR  - http://dx.doi.org/10.7494/OpMath.2008.28.3.325
AB  - A dominating set \(D \subset V(G)\) is a weakly connected dominating set in \(G\) if the subgraph \(G[D]_w = (N_{G}[D],E_w)\) weakly induced by \(D\) is connected, where \(E_w\) is the set of all edges with at least one vertex in \(D\). The weakly connected domination number \(\gamma_w(G)\) of a graph \(G\) is the minimum cardinality among all weakly connected dominating sets in \(G\). The graph is said to be weakly connected domination critical (\(\gamma_w\)-critical) if for each \(u, v \in V(G)\) with \(v\) not adjacent to \(u\), \(\gamma_w(G + vu) \lt \gamma_w (G)\). Further, \(G\) is \(k\)-\(\gamma_w\)-critical if \(\gamma_w(G) = k\) and for each edge \(e \not\in E(G)\), \(\gamma_w(G + e) \lt k\). In this paper we consider weakly connected domination critical graphs and give some properties of \(3\)-\(\gamma_w\)-critical graphs.
KW  - weakly connected domination number
KW  - tree
KW  - critical graphs
SN  - 1232-9274
ER  -