Results 11 to 20 of about 670,635 (308)
Double Roman Domination: A Survey
Mathematics, 2023 Since 2016, when the first paper of the double Roman domination appeared, the topic has received considerable attention in the literature. We survey known results on double Roman domination and some variations of the double Roman domination, and a list ...
Darja Rupnik Poklukar, Janez Žerovnik
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On The Roman Domination Stable Graphs
Discussiones Mathematicae Graph Theory, 2017 A Roman dominating function (or just RDF) on a graph G = (V,E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2.
Hajian Majid, Rad Nader Jafari
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Varieties of Roman domination II [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 In this work, we continue to survey what has been done on the Roman domination. More precisely, we will present in two sections several variations of Roman dominating functions as well as the signed version of some of these functions.
M. Chellali +3 more
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Perfect Roman Domination and Unique Response Roman Domination [PDF]
arXiv.org, 2023 The idea of enumeration algorithms with polynomial delay is to polynomially bound the running time between any two subsequent solutions output by the enumeration algorithm.
Henning Fernau, Kevin Mann
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Several Roman domination graph invariants on Kneser graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 This paper considers the following three Roman domination graph invariants on Kneser graphs: Roman domination, total Roman domination, and signed Roman domination.
Tatjana Zec, Milana Grbić
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Complexity of Roman {2}-domination and the double Roman domination in graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 For a simple, undirected graph a Roman {2}-dominating function (R2DF) has the property that for every vertex with f(v) = 0, either there exists a vertex with f(u) = 2, or at least two vertices with The weight of an R2DF is the sum The minimum weight of ...
Chakradhar Padamutham +1 more
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Powers of Large Matrices on GPU Platforms to Compute the Roman Domination Number of Cylindrical Graphs [PDF]
IEEE Access, 2021 The Roman domination in a graph G is a variant of the classical domination, defined by means of a so-called Roman domination function f : V (G) - {0, 1, 2} such that if f (v) = 0 then, the vertex v is adjacent to at least one vertex w with f (w) = 2. The
J. A. Martinez +2 more
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On [k] -Roman domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 For an integer [Formula: see text] let f be a function that assigns labels from the set [Formula: see text] to the vertices of a simple graph [Formula: see text].
N. Khalili +3 more
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On the Roman domination number of a graph
Discrete Mathematics, 2008 AbstractA Roman dominating function of a graph G is a labeling f:V(G)⟶{0,1,2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number γR(G) of G is the minimum of ∑v∈V(G)f(v) over such functions. A Roman dominating function of G of weight γR(G) is called a γR(G)-function.
Odile Favaron +3 more
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Integer Linear Programming Formulations for Triple and Quadruple Roman Domination Problems [PDF]
arXiv.org, 2023 Roman domination is a well researched topic in graph theory. Recently two new variants of Roman domination, namely triple Roman domination and quadruple Roman domination problems have been introduced, to provide better defense strategies. However, triple
Sanath Kumar Vengaldas +3 more
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