The Signed Total Roman k-Domatic Number Of A Graph

• Autorzy: Lutz Volkmann
• Języki publikacji: EN

Abstrakty

EN

Let k ≥ 1 be an integer. A signed total Roman k-dominating function on a graph G is a function f : V (G) → {−1, 1, 2} such that Ʃu2N(v) f(u) ≥ k for every v ∈ V (G), where N(v) is the neighborhood of v, and every vertex u ∈ V (G) for which f(u) = −1 is adjacent to at least one vertex w for which f(w) = 2. A set {f1, f2, . . . , fd} of distinct signed total Roman k-dominating functions on G with the property that Ʃdi=1 fi(v) ≤ k for each v ∈ V (G), is called a signed total Roman k-dominating family (of functions) on G. The maximum number of functions in a signed total Roman k-dominating family on G is the signed total Roman k-domatic number of G, denoted by dkstR(G). In this paper we initiate the study of signed total Roman k-domatic numbers in graphs, and we present sharp bounds for dkstR(G). In particular, we derive some Nordhaus-Gaddum type inequalities. In addition, we determine the signed total Roman k-domatic number of some graphs.

Słowa kluczowe

EN

signed total Roman k-dominating function; signed total Roman k-domination number; signed total Roman k-domatic number.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 4
• Strony: 1027-1038

Daty

wydano

2017-11-27

otrzymano

2016-03-14

poprawiono

2016-08-23

zaakceptowano

2016-08-23

online

2017-09-02

Twórcy

autor

Lutz Volkmann

• ,

Identyfikatory

DOI

10.7151/dmgt.1970