Signed star (k, k)-domatic number of a graph

• Autorzy: Sheikholeslami S. M. , Volkmann L.

Identyfikatory

DOI

http://dx.doi.org/10.7494/OpMath.2014.34.3.609

• 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 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.

Słowa kluczowe

EN

signed star (k, k)-domatic number; signed star domatic number; signed star k-dominating function; signed star dominating function; signed star k-domination number; signed star domination number; regular graphs

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2014
• Tom: Vol. 34, no. 3
• Strony: 609--620
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Sheikholeslami S. M.

• Azarbaijan Shahid Madani University Department of Mathematics Research Group of Processing and Communication Tabriz, I.R. Iran

autor

Volkmann L.

• RWTH-Aachen University Lehrstuhl II für Mathematik 52056 Aachen, Germany

Bibliografia

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