Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
418608 | Discrete Applied Mathematics | 2011 | 8 Pages |
Abstract
A graph GG with no isolated vertex is total domination vertex-critical if for any vertex vv of GG that is not adjacent to a vertex of degree one, the total domination number of G−vG−v is less than the total domination number of GG. A graph is total domination dot-critical if contracting any edge decreases the total domination number. In this paper, we study total domination dot-critical graphs. We present several properties of these graphs. We show that the total domination dot-critical graphs include the total domination vertex-critical graphs.
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Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Michael A. Henning, Nader Jafari Rad,