Signed star domatic number of a graph

Atapour, Masoud; Sheikholeslami, Seyed Mahmoud; Ghameshlou, Arezoo N.; Volkmann, Lutz

doi:10.1016/j.dam.2009.09.015

Cited by 7 publications

(6 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many of our results extend these given by Sheikholeslami and Volkmann [8] for the signed star (j, 1)-domatic number of digraphs. Using the associated digraph D(G) of a graph G, we also obtain bounds of Atapour, Sheikholeslami, Ghameslou and Volkmann [1] for the signed star domatic number d SS (G), Sheikholeslami and Volkmann [7] for the signed star (k, k)-domatic number d (k,k) SS (G), Sheikholeslami and Volkmann [6] for the signed star (j, k)-domatic number d (j,k) SS (G), and Sheikholeslami and Volkmann [5] for the signed star (j, 1)-domatic number d…”

Section: Introductionmentioning

confidence: 96%

See 1 more Smart Citation

Signed star (j, k)-domatic numbers of digraphs

Sheikholeslami

Volkmann

2015

Discrete Math. Algorithm. Appl.

Self Cite

View full text Add to dashboard Cite

Let D be a simple digraph with arc set A(D), and let j and k be two positive integers. A function f : A(D) → {-1, 1} is said to be a signed star j-dominating function (SSjDF) on D if ∑a ∈ A(v) f(a) ≥ j for every vertex v of D, where A(v) is the set of arcs with head v. A set {f1, f2, …, fd} of distinct SSjDFs on D with the property that [Formula: see text] for each a ∈ A(D), is called a signed star (j, k)-dominating (SS(j, k)D) family (of functions) on D. The maximum number of functions in a SS(j, k)D family on D is the signed star (j, k)-domatic number of D, denoted by [Formula: see text]. In this paper, we study properties of the signed star (j, k)-domatic number of a digraph D. In particular, we determine bounds on [Formula: see text]. Some of our results extend these ones given by Sheikholeslami and Volkmann [Signed star k-domination and k-domatic number of digraphs, submitted] for the signed (j, 1)-domatic number.

show abstract

Section: Introductionmentioning

confidence: 96%

“…Signed star (j, k)-domatic numbers of digraphs For graphs G the signed star (j, k)-domatic number was introduced by Sheikholeslami and Volkmann [6]. The signed star (1, 1)-domatic number d (1,1) SS (G) is the usual signed star domatic number d SS (G), which was introduced by Atapour, Sheikholeslami, Ghameshlou and Volkmann [1] in 2010.…”

Section: Introductionmentioning

confidence: 98%

Signed star (j, k)-domatic numbers of digraphs

Sheikholeslami

Volkmann

2015

Discrete Math. Algorithm. Appl.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The special case k = 1 in Proposition 2.1 can be found in [1]. As an application of Proposition 2.1, we will prove the following Nordhaus-Gaddum type result.…”

Section: Basic Properties Of the Signed Star (K K)-domatic Numbermentioning

confidence: 99%

“…We first study basic properties and bounds for the signed star (k, k)-domatic number of a graph where some of them are analogous to those of the signed star domatic number d SS (G) in [1]. In addition, we determine the signed star (k, k)-domatic number of some regular graphs.…”

Section: Introductionmentioning

confidence: 99%