Weak signed Roman k-domination in digraphs

• Autorzy: Volkmann Lutz

Identyfikatory

DOI

10.7494/OpMath.2024.44.2.285

• Języki publikacji: EN

Abstrakty

EN

Let k ≥ 1 be an integer, and let D be a finite and simple digraph with vertex set V (D). A weak signed Roman k-dominating function (WSRkDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the condition that ∑x∈N−[v] f(x) ≥ k 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 WSRkDF f is w(f) = ∑v∈V (D) f(v). The weak signed Roman k-domination number [formula] is 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 [formula]. 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 [formula] and the signed Roman k-domination number [formula].

Słowa kluczowe

EN

digraph; weak signed Roman k-dominating function; weak signed Roman k-domination number; signed Roman k-dominating function; signed Roman k-domination number

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 2
• Strony: 285--296
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Volkmann Lutz

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

Bibliografia

• [1] H. Abdollahzadeh Ahangar, M.A. Henning, C. Löwenstein, Y. Zhao, V. Samodivkin, Signed Roman domination in graphs, J. Comb. Optim. 27 (2014), no. 2, 241–255.
• [2] M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, L. Volkmann, A survey on Roman parameters in directed graph, J. Combin. Math. Combin. Comput. 115 (2020), 141–171.
• [3] G. Hao, X. Chen, L. Volkmann, Bounds on the signed Roman k-domination number of a digraph, Discuss. Math. Graph Theory 39 (2019), 67–79.
• [4] T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998.
• [5] T.W. Haynes, S.T. Hedetniemi, P.J. Slater (eds), Domination in Graphs: Advanced Topics, Marcel Dekker, Inc., New York, 1998.
• [6] M.A. Henning, L. Volkmann, Signed Roman k-domination in graphs, Graphs Combin. 32 (2016), 175–190.
• [7] S.M. Sheikholeslami, L. Volkmann, Signed Roman domination in digraphs, J. Comb. Optim. 30 (2015), no. 3, 456–467.
• [8] L. Volkmann, Signed Roman k-domimation in digraphs, Graphs Combin. 32 (2016), 1217–1227.
• [9] L. Volkmann, Weak signed Roman domination in graphs, Commun. Comb. Optim. 5 (2020), no. 2, 111–123.
• [10] L. Volkmann, Weak signed Roman k-domination in graphs, Commun. Comb. Optim. 6 (2021), no. 1, 1–15.
• [11] L. Volkmann, Weak signed Roman domination in digraphs, Tamkang J. Math. 52 (2021), no. 4, 497–508.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)