@Article{Lemańska2008,
author = "Lemańska, Magdalena and Patyk, Agnieszka",
title = "Weakly connected domination critical graphs",
journal = "Opuscula Math.",
year = "2008",
volume = "28",
number = "3",
pages = "325--330",
doi = "http://dx.doi.org/10.7494/OpMath.2008.28.3.325",
url = "http://dx.doi.org/10.7494/OpMath.2008.28.3.325",
abstract = "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.",
keywords = "weakly connected domination number, tree, critical graphs",
issn = "1232-9274"
}