Powiadomienia systemowe
- Sesja wygasła!
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Let G be a simple graph without isolated vertices with vertex set V (G) and edge set E(G) and let k be a positive integer. A function ƒ: E(G) →{−1, 1} is said to be a signed star k-dominating function on [formula] for every vertex v of G, where E(v) = {uv ∈ E(G) | u ∈ N(v)}. A set {f1, f2, . . . , fd} of signed star k-dominating functions on G with the property that [formula] for each e ∈ E(G) is called a signed star (k, k)-dominating family (of functions) on G. The maximum number of functions in a signed star (k, k)-dominating family on G is the signed star (k, k)-domatic number of G, denoted by [formula]. In this paper we study properties of the signed star (k, k)-domatic number [formula]. In particular, we present bounds on [formula], and we determine the signed (k, k)-domatic number of some regular graphs. Some of our results extend these given by Atapour, Sheikholeslami, Ghameslou and Volkmann [Signed star domatic number of a graph, Discrete Appl. Math. 158 (2010), 213–218] for the signed star domatic number.
Czasopismo
Rocznik
Tom
Strony
609--620
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Azarbaijan Shahid Madani University Department of Mathematics Research Group of Processing and Communication Tabriz, I.R. Iran
autor
- RWTH-Aachen University Lehrstuhl II für Mathematik 52056 Aachen, Germany
Bibliografia
- [1] M. Atapour, S.M. Sheikholeslami, A.N. Ghameshlou, L. Volkmann, Signed star domatic number of a graph, Discrete Appl. Math. 158 (2010), 213–218.
- [2] T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamentals of Domination in graphs, Marcel Dekker, Inc., New York, 1998.
- [3] D. König, Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre, Math. Ann. 77 (1916), 453–465.
- [4] R. Saei, S.M. Sheikholeslami, Signed star k-subdomination numbers in graphs, Discrete Applied Math. 156 (2008), 3066–3070.
- [5] S.M. Sheikholeslami, L. Volkmann, Signed star k-domatic number of a graph, Contrib. Discrete Math. 6 (2011), 20–31.
- [6] C.P. Wang, The signed star domination numbers of the Cartesian product, Discrete Appl. Math. 155 (2007), 1497–1505.
- [7] C.P. Wang, The signed b-matchings and b-edge covers of strong product graphs, Contrib. Discrete Math. 5 (2010), 1–10.
- [8] D.B. West, Introduction to Graph Theory, Prentice-Hall, Inc., 2000.
- [9] B. Xu, On edge domination numbers of graphs, Discrete Math. 294 (2005), 311–316.
- [10] B. Xu, Two classes of edge domination in graphs, Discrete Appl. Math. 154 (2006), 1541–1546.
- [11] B. Xu, C.H. Li, Signed star k-domination numbers of graphs, Pure Appl. Math. (Xi’an) 25 (2009), 638–641 [in Chinese].
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c22f168b-18d7-4197-8c74-cfeac7c384ac