Weak signed Roman k-domination in digraphs

Opuscula Mathematica, vol. 44, pp. 285–296

Abstract

Let k ≥ 1 be an integer, and let D be a finite and simple digraph withis the minimum weight of a WSRkDF on D. In this paper we initiate the study of the weak signed Roman k-domination number of digraphs, and we present different bounds on γ k wsR (D).In addition, we determine the weak signed Roman k-domination number of some classes of digraphs.Some of our results are extensions of well-known properties of the weak signed Roman domination number γ wsR (D) = γ 1 wsR (D) and the signed Roman k-domination number γ k sR (D).

Authors 1

1. Lutz Volkmann corresponding Aachen Lehrstuhl II für Mathematik

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl II für Mathematik RWTH Aachen University 52056 Aachen, Germany