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Complexity and Exact Values for [k]-Roman and Strong Roman Domination for Specific Graph Families
MathematicsMotivated by the original idea of defending the Roman Empire, all these domination concepts can be interpreted as vertex-labeling schemes that model the allocation of resources to protect a graph against attacks.
Juan Carlos Valenzuela-Tripodoro +3 more
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A note on the independent roman domination in unicyclic graphs [PDF]
Opuscula Mathematica, 2012 A Roman dominating function (RDF) on a graph \(G = (V;E)\) is a function \(f : V \to \{0, 1, 2\}\) satisfying the condition that every vertex \(u\) for which \(f(u) = 0\) is adjacent to at least one vertex \(v\) for which \(f(v) = 2\).
Mustapha Chellali, Nader Jafari Rad
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Bounds on the Double Italian Domination Number of a Graph
Discussiones Mathematicae Graph Theory, 2022 For a graph G, a Roman {3}-dominating function is a function f : V → {0, 1, 2, 3} having the property that for every vertex u ∈ V, if f(u) ∈ {0, 1}, then f(N[u]) ≥ 3.
Azvin Farzaneh, Rad Nader Jafari
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On the Total Version of Triple Roman Domination in Graphs
MathematicsIn this paper, we describe the study of total triple Roman domination. Total triple Roman domination is an assignment of labels from {0,1,2,3,4} to the vertices of a graph such that every vertex is protected by at least three units either on itself or ...
Juan Carlos Valenzuela-Tripodoro +3 more
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Angewandte Chemie, EarlyView.Cement‐mimetic hydraulicity is realized in an organic polymer through a counterintuitive reaction in which a hydrophilic linear polymer reacts with water to undergo hydrophobization during curing via silatrane sol–gel chemistry. This polarity‐inverting curing process turns a water‐plasticized putty into a water‐tolerant rigid material, enabling ...
Rei Tokumitsu +3 more
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Triple Roman domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2022 For a graph $G=(V, E)$, a triple Roman domination function is a function $f: V(G)\longrightarrow\{0, 1, 2, 3, 4\}$ having the property that for any vertex $v\in V(G)$, if $f(v)
Jafar Amjadi, Hakimeh Sadeghi
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On the total Roman domination in trees
Discussiones Mathematicae Graph Theory, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amjadi Jafar +2 more
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On the co-Roman domination in graphs
Discussiones Mathematicae Graph Theory, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zehui Shao +4 more
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Advanced Materials, EarlyView.This work investigates the heterogeneous nucleation of CsPbBr3${\rm CsPbBr}_3$ nanocrystal superlattices along the faces of 2D PEA2PbBr4${\rm PEA}_2{\rm PbBr}_4$ layered perovskite microcrystals. Core–crown and core–shell heterostructure morphologies are obtained.
Umberto Filippi +6 more
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Some Progress on the Double Roman Domination in Graphs
Discussiones Mathematicae Graph Theory, 2019 For a graph G = (V,E), a double Roman dominating function (or just DRDF) is a function f : V → {0, 1, 2, 3} having the property that if f(v) = 0 for a vertex v, then v has at least two neighbors assigned 2 under f or one neighbor assigned 3 under f, and ...
Rad Nader Jafari, Rahbani Hadi
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