Signed total Roman k-domination in directed graphs

Document Type : Original paper

Authors

1 Sirjan University of Technology, Sirjan 78137, Iran

2 Lehrstuhl II fur Mathematik, RWTH Aachen University, 52056 Aachen, Germany

Abstract

Let D be a finite and simple digraph with vertex set V(D). A signed total Roman k-dominating function (STRkDF) on D is a function f:V(D)→{−1,1,2} satisfying the conditions that (i) ∑x∈N−(v)f(x)≥k for each v∈V(D), where N−(v) consists of all vertices of D from which arcs go into v, and (ii) every vertex u for which f(u)=−1 has an inner neighbor v for which f(v)=2. The weight of an STRkDF f is ω(f)=∑v∈V(D)f(v). The signed total Roman k-domination number γstRk(D) of D is the minimum weight of an STRkDF on D. In this paper we initiate the study of the signed total Roman k-domination number of digraphs, and we present different bounds on γstRk(D). In addition, we determine the signed total Roman k-domination number of some classes of digraphs. Some of our results are extensions of known properties of the signed total Roman k-domination number γstRk(G) of graphs G.

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References

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Communications in Combinatorics and Optimization
Volume 1, Issue 2 - Serial Number 2
December 2016
Pages 165-178

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