Article ID Journal Published Year Pages File Type
4651259 Discrete Mathematics 2006 8 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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