Czechoslovak Mathematical Journal

, Volume 59, Issue 1, pp 95–100 | Cite as

Weakly connected domination stable trees

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Abstract

A dominating set D ⊆ 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 having at least one vertex in D. Weakly connected domination number γw (G) of a graph G is the minimum cardinality among all weakly connected dominating sets in G. A graph G is said to be weakly connected domination stable or just γw -stable if γw (G) = γ w (G + e) for every edge e belonging to the complement Ḡ of G. We provide a constructive characterization of weakly connected domination stable trees.

Keywords

weakly connected domination number tree stable graphs 

MSC 2000

05C05 05C69 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2009

Authors and Affiliations

  1. 1.Department of Applied Physics and MathematicsGdańsk University of TechnologyGdańskPoland

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