Upper Bounds on the Signed Total (K, K)-Domatic Number of Graphs
Lutz Volkmann
Discussiones Mathematicae Graph Theory, Tome 35 (2015), p. 641-650 / Harvested from The Polish Digital Mathematics Library
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Let G be a graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and Σx∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {f1, f2, . . . , fd} of distinct signed total k-dominating functions on G with the property that Σdi=1 fi(x) ≤ k for each x ∈ V (G), is called a signed total (k, k)-dominating family (of functions) on G. The maximum number of functions in a signed total (k, k)-dominating family on G is the signed total (k, k)-domatic number of G. In this article we mainly present upper bounds on the signed total (k, k)- domatic number, in particular for regular graphs.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:276003 
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     volume = {35},
     year = {2015},
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     zbl = {1327.05267},
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Lutz Volkmann. Upper Bounds on the Signed Total (K, K)-Domatic Number of Graphs. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 641-650. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1823/

[1] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, 1998). | Zbl 0890.05002

[2] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Ed(s), Domination in Graphs, Advanced Topics (Marcel Dekker, Inc., New York, 1998). | Zbl 0883.00011

[3] M.A. Henning, Signed total domination in graphs, Discrete Math. 278 (2004) 109-125. doi:10.1016/j.disc.2003.06.002[Crossref]

[4] M.A. Henning, On the signed total domatic number of a graph, Ars Combin. 79 (2006) 277-288. | Zbl 1164.05421

[5] S.M. Sheikholeslami and L. Volkmann, Signed total (k, k)-domatic number of a graph, AKCE Int. H. J. Graphs Comb. 7 (2010) 189-199. | Zbl 1248.05143

[6] C. Wang, The signed k-domination numbers in graphs, Ars Combin. 106 (2012) 205-211. | Zbl 1289.05363

[7] B. Zelinka, Signed total domination number of a graph, Czechoslovak. Math. J. 51 (2001) 225-229. doi:10.1023/A:1013782511179 [Crossref] | Zbl 0977.05096