Journal
DISCRETE MATHEMATICS
Volume 306, Issue 1, Pages 11-18Publisher
ELSEVIER
DOI: 10.1016/j.disc.2005.06.029
Keywords
tree; domination; critical; corona
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A graph G is dot-critical if contracting any edge decreases the domination number. It is totally dot-critical if identifying any two vertices decreases the domination number. We show that the totally dot-critical graphs essentially include the much-studied domination vertex-critical and edge-critical graphs as special cases. We investigate these properties, and provide a characterization of dot-critical and totally dot-critical graphs with domination number 2. We also consider the question of when a dot-critical graph contains a critical vertex. (c) 2005 Elsevier B.V. All rights reserved.
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