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Bounds on total domination in claw-free cubic graphs
2008
Discrete Mathematics
A set S of vertices in a graph G is a total dominating set, denoted by TDS, of G if every vertex of G is adjacent to some vertex in S (other than itself). The minimum cardinality of a TDS of G is the total domination number of G, denoted by t (G). If G does not contain K 1,3 as an induced subgraph, then G is said to be claw-free. It is shown in [Some remarks on domination, J. Graph Theory 46 (2004) 207-210.] that if G is a graph of order n with minimum degree at least three, then t (G) n/2. Two
doi:10.1016/j.disc.2007.07.007
fatcat:3ayowy544veadgrxyxlfekmvsu