Article

The diameter of total domination vertex critical graphs.

Discrete Mathematics 01/2004; 286:255-261. DOI: 10.1016/j.disc.2004.05.010
Source: DBLP

ABSTRACT A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G v is less than the total domination number of G. These graphs we call t-critical. If such a graph G has total domination number k, we call it k-t-critical. We characterize the connected graphs with minimum degree one that are t-critical and we obtain sharp bounds on their maximum diameter. We calculate the maximum diameter of a k-t-critical graph for k � 8 and provide an example which shows that the maximum diameter is in general at least 5k/3 O(1).

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