Total domination critical and stable graphs upon edge removal |
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Authors: | Wyatt J. Desormeaux Michael A. Henning |
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Affiliation: | a Department of Mathematics, East Tennessee State University, Johnson City, TN 37614-0002, USA b Department of Mathematics, University of Johannesburg, Auckland Park 2006, South Africa |
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Abstract: | A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination edge critical if the removal of any arbitrary edge increases the total domination number. On the other hand, a graph is total domination edge stable if the removal of any arbitrary edge has no effect on the total domination number. In this paper, we characterize total domination edge critical graphs. We also investigate various properties of total domination edge stable graphs. |
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Keywords: | Total domination edge critical Total domination edge stable |
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