Vertices contained in all or in no minimum total dominating set of a tree
Discrete Mathematics
Total domination excellent trees
Discrete Mathematics
Upper signed k-domination in a general graph
Information Processing Letters
Discrete Applied Mathematics
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A set S of vertices of a graph G is a total dominating set, if every vertex of V(G) is adjacent to some vertex in S. The total domination number of G, denoted by γt(G), is the minimum cardinality of a total dominating set of G. We prove that, if G is a graph of order n with minimum degree at least 3, then γt(G) ≤ 7n-13. © 2000 John Wiley & Sons, Inc. J Graph Theory 34:9–19, 2000 This article was written while the first and fourth authors were visiting the University of Sourth Africa supported by a grant under the Franco-South African Agreement for Co-operation in Science and Engineering.