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Details for article 9 of 9 found articles
| Title: |
Weakly connected domination critical graphs |
| Author: |
Magdalena Lemańska Agnieszka Patyk |
| Appeared in: |
Opuscula mathematica |
| Paging: | Volume 28 (2008) nr. 3 pages 325-330 |
| Year: |
2008 |
| Contents: |
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 $u$, $\gamma_w(G + vu) < \gamma_w (G)$. Further, $G$ is k-$\gamma_w$-critical if $\gamma_w(G) = k$ and for each edge $e \nin E(G)$, $\gamma_w(G + e) < k$. In this paper we consider weaklyconnected domination critical graphs and give some properties of 3-$\gamma_w$-critical graphs. |
| Publisher: |
AGH University of Science and Technology (provided by DOAJ) |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 9 of 9 found articles
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