Signed total Italian k-domination in digraphs

Document Type : Original paper

Author

Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany

Abstract

Let k≥1 be an integer, and let D be a finite and simple digraph with vertex set V(D). A signed total Italian k-dominating function (STIkDF) on a digraph D is a function f:V(D)→{−1,1,2} satisfying the conditions that (i) ∑x∈N−(v)f(x)≥k for each vertex v∈V(D), where N−(v) consists of all vertices of D from which arcs go into v, and (ii) each vertex u with f(u)=−1 has an in-neighbor v for which f(v)=2 or two in-neighbors w and z with f(w)=f(z)=1. The weight of an STIkDF f is ω(f)=∑v∈V(D)f(v). The signed total Italian k-domination number γstIk(D) of D is the minimum weight of an STIkDF on D. In this paper we initiate the study of the signed total Italian k-domination number of digraphs, and we  present different bounds on γstIk(D). In addition, we determine the signed total Italian k-domination number of some classes of digraphs.

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References

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Communications in Combinatorics and Optimization
Volume 9, Issue 2
June 2024
Pages 339-351

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