Geodesic
New Bounds on the Signed Total Domination Number of Graphs
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 2, pp. 467-477

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In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on K_r+1-free graphs for r ≥ 2. Applying the concept of total limited packing we bound the signed total domination number of G with δ (G) ≥ 3 from above by n - 2 2 ρ_0 (G) + δ - 3 / 2. Also, we prove that γ_st (T) ≤ n − 2(s − s^′ ) for any tree T of order n, with s support vertices and s^′ support vertices of degree two. Moreover, we characterize all trees attaining this bound.
Keywords: open packing, signed total domination number, total limited packing, tuple total domination number 
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Moghaddam, Seyyed Mehdi Hosseini; Mojdeh, Doost Ali; Samadi, Babak; Volkmann, Lutz. New Bounds on the Signed Total Domination Number of Graphs. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 2, pp. 467-477. http://geodesic.mathdoc.fr/item/DMGT_2016_36_2_a16/