Total domination critical and stable graphs upon edge removal

Authors:
Wyatt J. Desormeaux;Teresa W. Haynes;Michael A. Henning
Affiliations:
Department of Mathematics, University of Johannesburg, Auckland Park 2006, South Africa;Department of Mathematics, East Tennessee State University, Johnson City, TN 37614-0002, USA;Department of Mathematics, University of Johannesburg, Auckland Park 2006, South Africa
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 1
Cited 3

Graphs with large total domination number

Journal of Graph Theory

Note: An extremal problem for total domination stable graphs upon edge removal

Discrete Applied Mathematics
Total domination changing and stable graphs upon vertex removal

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Edge lifting and total domination in graphs

Journal of Combinatorial Optimization

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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.