Research Article

Further results on the independent Roman domination number of graphs

Published in: Quaestiones Mathematicae
Volume 46 , issue 2 , 2023 , pages: 347–357

DOI: 10.2989/16073606.2021.2014595

Author(s): Abel Cabrera Martínez Universitat Rovira i Virgili, Spain , Frank A. Hernández Mira Universidad Autónoma de Guerrero, México

Keywords: Primary: 05C69 , Secondary: 05C76 , Independent Roman domination number , independent domination number , independence number , product graphs

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Abstract

Let f : V (G) → {0, 1, 2} be a function on a graph G with vertex set V (G). Let V_i = {v ∈ V (G) : f (v) = i} for every i ∈ {0, 1, 2}. The function f is said to be an independent Roman dominating function on G if V ₁ ∪ V ₂ is an independent set and for every υ 2 V ₀. The minimum weight among all independent Roman dominating functions f on G is the independent Roman domination number of G, and is denoted by i_R (G). In this paper we continue with the study of this parameter. In particular, we provide new bounds on i_R (G) in terms of other domination invariants. Some of our results are tight bounds that improve some well-known results. Finally, we compute the independent Roman domination number of some product graphs, and we provide an alternative proof to show that the problem of computing i_R (G) is NP-hard.

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