Properties of total domination edge-critical graphs

Authors:
Michael A. Henning;Lucas C. van der Merwe
Affiliations:
School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209, South Africa;Department of Mathematics, University of Tennessee in Chattanooga, Chattanooga, TN 37403, USA
Venue:
Discrete Applied Mathematics
Year:
2010

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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 @c"t(G) of G. The graph G is total domination edge critical if for every edge e in the complement of G, @c"t(G+e)