Powiadomienia systemowe
- Sesja wygasła!
Tytuł artykułu
Wybrane pełne teksty z tego czasopisma
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 f : E(G) —> {±1, ±2,..., ±k} is said to be a signed star {k}-dominating function on G if Σe∈E(v) ≥ k for every vertex v of G, where E(v) = {uv ∈ E(G) | u ∈ N(v)}. The signed star {k}-domination number of a graph G is y{k}ss(G) = min{ Σe∈Ef(v) | f is a SS{k}DF on G}. A set {f1, f2,..., fd} of distinct signed star {k}-dominating functions on G with the property that …[wzór] for each e ∈ E(G), is called a signed star {k}-dominating family (of functions) on G. The maximum number of functions in a signed star {k}-dominating family on G is the signed star {k}-domatic number of G, denoted by d{k}SS(G). In this paper we study the properties of the signed star {k}- domination number y{k}SS(G) and signed star {k}-domatic number d{k}SS(G). In particular, we determine the signed star {k}-domination number of some classes of graphs. Some of our results extend these one given by Xu [7] for the signed star domination number and Atapour et al. [1] for the signed star domatic number.
Czasopismo
Rocznik
Tom
Strony
33--43
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
- Department of Mathematics Azarbaijan Shahid Madani University Tabriz, I.R. Iran
autor
- Department of Mathematics Azarbaijan Shahid Madani University Tabriz, I.R. Iran
autor
- Lehrstuhl II für Mathematik RWTH-Aachen University 52056 Aachen, Germany
Bibliografia
- [1] Atapour M., Sheikholeslami S.M., Ghameshlou A.N., Yolkmann L., Signed star domatic number of a graph, Discrete Appl. Math., 158(2010), 213-218.
- [2] Haynes T.W., Hedetniemi S.T., Slater P.J., Fundamentals of Domination in graphs, Marcel Dekker, Inc., New York, 1998.
- [3] König D., Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre, Math. Ann., 77(1916), 453-465.
- [4] Saei R., Sheikholeslami S.M., Signed star k-subdomination numbers in graphs, Discrete Appl. Math., 156(2008), 3066-3070.
- [5] Wang C., The signed star domination numbers of the Cartesian product, Discrete Appl. Math., 155(2007), 1497-1505.
- [6] West D.B., Introduction to Graph Theory, Prentice-Hall, Inc, 2000.
- [7] Xu B., On edge domination numbers of graphs, Discrete Math., 294(2005), 311-316.
- [8] Xu B., Two classes of edge domination in graphs, Discrete Appl. Math., 154 (2006), 1541-1546.
- [9] Xu B., Li C.H., Signed star k-domination numbers of graphs, (Chinese) Pure Appl. Math. (Xi’an), 25(2009), 638-641.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9c3019df-88a8-4255-90e3-3a7f7fe8406e