Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651259 | Discrete Mathematics | 2006 | 8 Pages |
Abstract
A graph GG 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Tamara Burton, David P. Sumner,