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- Title
Weak Signed Roman Domination in Digraphs.
- Authors
Volkmann, Lutz
- Abstract
LetD be a finite and simple digraph with vertex set V (D). A weak signed Roman dominating function (WSRDF) on a digraph D is a function f: V (D) → {−1, 1, 2} satisfying the condition that Σ x∈N−[v] f(x) ≥ 1 for each v ∈ V (D), where N−[v] consists of v and all vertices of D from which arcs go into v. The weight of a WSRDF f is Σ v∈V (D) f(v). The weak signed Roman domination number γwsR(D) of D is the minimum weight of a WSRDF on D. In this paper we initiate the study of the weak signed Roman domination number of digraphs, and we present different bounds on γwsR(D). In addition, we determine the weak signed Roman domination number of some classes of digraphs.
- Subjects
DIRECTED graphs; MATHEMATICAL constants; MATHEMATICS theorems; GEOMETRIC vertices; ROMAN numerals
- Publication
Tamkang Journal of Mathematics, 2021, Vol 52, Issue 4, p497
- ISSN
0049-2930
- Publication type
Article
- DOI
10.5556/j.tkjm.52.2021.3523