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A note on the double Roman domination number of graphs [PDF]
, 2017 summary:For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least two neighbors assigned $2$ under $f$ or one neighbor with $f(w)
Chen, Xue-Gang +3 more
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Roman Domination Cover Rubbling [PDF]
, 2019 In this thesis, we introduce Roman domination cover rubbling as an extension of domination cover rubbling. We define a parameter on a graph $G$ called the \textit{Roman domination cover rubbling number}, denoted $\rho_{R}(G)$, as the smallest number of ...
Carney, Nicholas
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Trees with vertex-edge Roman Domination number twice the domination number minus one
, 2020 A vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V, E) is a function f : V (G) → {0, 1, 2} such that for each edge e = uv either max{f (u), f (v)} ≠ 0 or there exists a vertex w such that either wu ∈ E or wv ∈ E and f (w) = 2. The
Venkatakrishnan, Y. B., Naresh Kumar, H.
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Double Roman reinforcement number in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 For a graph a double Roman dominating function is a function having the property that if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(v) = 1, then vertex v must have at least one ...
J. Amjadi, H. Sadeghi
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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
wiley +2 more sources
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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Domination parameters: Roman domination number
, 2022 Tezin 1. bölümünde, baskınlık sayısı ve Roman baskınlık sayısı tanımları verilerek, bu kavramlar günlük yaşamdan örnekler ile açıklanmıştır. Ardından Roman baskınlık sayısı için literatürde yer alan bazı sonuçlar verilmiştir. Tezin 2.
Zaim, Nurdan
core
[k]-Roman Domination in Digraphs
, 2023 Let D=(V(D),A(D)) be a finite, simple digraph and k a positive integer. A function f:V(D)→{0,1,2,…,k+1} is called a [k]-Roman dominating function (for short, [k]-RDF) if f(AN−[v])≥|AN−(v)|+k for any vertex v∈V(D), where AN&
Ruijuan Li, Xinhong Zhang, Xin Song
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Angewandte Chemie, EarlyView.Increasing the density of isolated manganese (Mn) atoms in carbon nitride (CNx) photocatalysts does not continuously improve performance. Instead, beyond a critical loading, the polymer support reorganizes, altering charge‐carrier dynamics and oxygen activation while preserving atomic dispersion.
Viktoria Velichko +14 more
wiley +2 more sources
Total Roman Domination Number of Rooted Product Graphs
Mathematics, 2020 Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. If f satisfies that every vertex in the set {v∈V(G):f(v)=0} is adjacent to at least one vertex in the set {v∈V(G):f(v)=2}, and if the subgraph induced by the set {v∈V(G):f(v)≥1} has ...
Abel Cabrera Martínez +3 more
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