Weakly connected domination critical graphs

• Autorzy: Lemańska M. , Patyk A.
• Języki publikacji: EN

Abstrakty

EN

A dominating set D ⊂ V(G) is a weakly connected dominating set in G if the subgraph G[D]w = (NG[D], Ew) weakly induced by D is connected, where Ew is the set of all edges with at least one vertex in D. The weakly connected domination number ϒw(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 (ϒw-critical) if for each u, v ∈ V(G) with v not adjacent to u, ϒw(G + vu) < ϒw(G). Further, G is k- ϒw-critical if ϒw(G) = k and for each edge e ∉ E(G), ϒw(G + e) < k. In this paper we consider weakly connected domination critical graphs and give some properties of 3-ϒw,-critical graphs.

Słowa kluczowe

EN

weakly connected domination number; tree; critical graphs

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2008
• Tom: Vol. 28, no. 3
• Strony: 325--330
• Opis fizyczny: Bibliogr.4 poz., rys.

Twórcy

autor

Lemańska M.

autor

Patyk A.

• Gdansk University of Technology, Department of Technical Physics and Applied Mathematics, Narutowicza 11/12, 80-952 Gdansk, Poland,

Bibliografia

• [1] J. Dunbar, J. Grossman, S.T. Hedetniemi, J.H. Hatting, A. McRae, On weakly-connected domination in graphs, Discrete Mathematics 167–168 (1997), 261–269.
• [2] X-G. Chen, L. Sun, D-X. Ma, Connected domination critical graphs, Applied Mathematics Letters 17 (2004), 503–507.
• [3] D.P. Sumner, P. Blitch, Domination critical graphs, J. Combin. Theory Ser. B 34 (1983), 65–76.
• [4] M. Lemanska, Domination numbers in graphs with removed edge or set of edges, Disscussiones Mathematicae Graph Theory 25 (2005), 51–56.