Copyright © 2004 Elsevier B.V. All rights reserved.
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The diameter of total domination vertex critical graphs
Received 23 May 2002;
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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 γt-critical. If such a graph G has total domination number k, we call it k-γt-critical. We characterize the connected graphs with minimum degree one that are γt-critical and we obtain sharp bounds on their maximum diameter. We calculate the maximum diameter of a k-γt-critical graph for k
8 and provide an example which shows that the maximum diameter is in general at least 5k/3-O(1).
Keywords: Total domination; Vertex critical; Bounds; Diameter
MSC: 05C69






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