The Diameter of Total Domination Vertex Critical Graphs
Document Type
Article
Publication Date
9-28-2004
Description
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 γ t-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).
Citation Information
Goddard, Wayne; Haynes, Teresa W.; Henning, Michael A.; and Van der Merwe, Lucas C.. 2004. The Diameter of Total Domination Vertex Critical Graphs. Discrete Mathematics. Vol.286(3). 255-261. https://doi.org/10.1016/j.disc.2004.05.010 ISSN: 0012-365X