Signed star {k}-domatic number of a graph

• Autorzy: Atapour M. , Sheikholeslami S. M. , Volkmann L.
• Języki publikacji: EN

Abstrakty

EN

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 Σ_e∈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{ Σ_e∈Ef(v) | f is a SS{k}DF on G}. A set {f₁, f₂,..., f_d} 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.

Słowa kluczowe

EN

signed star {k}-domatic number; signed star domatic number; signed star k-dominating function; signed star dominating functions; signed star {k}-domination number; signed star domination number; regular graphs

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2013
• Tom: Nr 51
• Strony: 33--43
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Atapour M.

• Department of Mathematics Azarbaijan Shahid Madani University Tabriz, I.R. Iran

autor

Sheikholeslami S. M.

• Department of Mathematics Azarbaijan Shahid Madani University Tabriz, I.R. Iran

autor

Volkmann L.

• 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.