Discrete Mathematics
Vertices contained in all or in no minimum total dominating set of a tree
Discrete Mathematics
Total domination excellent trees
Discrete Mathematics
Total domination in partitioned trees and partitioned graphs with minimum degree two
Journal of Global Optimization
Total domination critical and stable graphs upon edge removal
Discrete Applied Mathematics
Total domination dot-critical graphs
Discrete Applied Mathematics
Note: Total domination dot-stable graphs
Discrete Applied Mathematics
Note: An extremal problem for total domination stable graphs upon edge removal
Discrete Applied Mathematics
Total domination changing and stable graphs upon vertex removal
Discrete Applied Mathematics
On α-total domination in graphs
Discrete Applied Mathematics
The total bondage number of grid graphs
Discrete Applied Mathematics
Discrete Applied Mathematics
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Let G = (V,E) be a graph. A set S⊆ V is a total dominating set if every vertex ofV is adjacent to some vertex in S. The totaldomination number of G, denoted byΥt(G), is the minimum cardinalityof a total dominating set of G. We establish a property ofminimum total dominating sets in graphs. If G is a connectedgraph of order n ≥ 3, then (see [3])Υt(G) ≤ 2n-3. We showthat if G is a connected graph of order n withminimum degree at least 2, then eitherΥt(G) ≤ 4n-7 or Gε {C3, C5,C6, C10}. A characterization ofthose graphs of order n which are edge-minimal with respectto satisfying G connected, δ(G) e 2 andΥt(G) ≥ 4n-7 isobtained. We establish that if G is a connected graph ofsize q with minimum degree at least 2, thenΥt(G) ≤(q + 2)-2.Connected graphs G of size q with minimum degree atleast 2 satisfying Υt(G) q-2 are characterized. © 2000 John Wiley & Sons,Inc. J Graph Theory 35: 2145, 2000