On algorithmic complexity of double Roman domination

Poureidi, Abolfazl; Rad, Nader Jafari

doi:10.1016/j.dam.2020.06.023

Cited by 10 publications

(3 citation statements)

References 11 publications

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“…First, to show that this decision problem for maximal double Roman domination is NPcomplete, we use a polynomial time reduction from the double Roman domination problem shown to be NP-complete for bipartite and chordal graphs in [4], and for planar graphs in [16]. Proof.…”

Section: Complexity Resultsmentioning

confidence: 99%

Maximal double Roman domination in graphs

Ahangar

Chellali

Sheikholeslami

et al. 2022

Applied Mathematics and Computation

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Section: Complexity Resultsmentioning

confidence: 99%

Maximal double Roman domination in graphs

Ahangar

Chellali

Sheikholeslami

et al. 2022

Applied Mathematics and Computation

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“…Special case k = 2, the double Roman domination, is considered in this work. It is well-known that the decision version of the double Roman domination problem (MIN-DOUBLE-RDF) is NP-complete, even when restricted to planar graphs, chordal graphs, bipartite graphs, undirected path graphs, chordal bipartite graphs and to circle graphs [7][8][9]. It is therefore of interest to study the complexity of the problem for other families of graphs.…”

Section: Introductionmentioning

confidence: 99%

“…It is therefore of interest to study the complexity of the problem for other families of graphs. For example, linear time algorithms exist for interval graphs and block graphs [8], for trees [10], for proper interval graphs [11] and for unicyclic graphs [9]. Another avenue of research that is motivated by high complexity of the problem is to obtain closed expressions for the double Roman domination number of some families of graphs.…”

Section: Introductionmentioning

confidence: 99%

On the Double Roman Domination in Generalized Petersen Graphs P(5k,k)

Poklukar

Žerovnik

2022

Mathematics

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A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and every vertex u with f(u)=1 is adjacent to at least one vertex assigned 2 or 3. The weight of f equals w(f)=∑v∈Vf(v). The double Roman domination number γdR(G) of a graph G equals the minimum weight of a double Roman dominating function of G. We obtain closed expressions for the double Roman domination number of generalized Petersen graphs P(5k,k). It is proven that γdR(P(5k,k))=8k for k≡2,3mod5 and 8k≤γdR(P(5k,k))≤8k+2 for k≡0,1,4mod5. We also improve the upper bounds for generalized Petersen graphs P(20k,k).

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