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Total Roman \{2\} -dominating functions in graphs
Discussiones Mathematicae Graph Theory, 2020 A Roman $\{2\}$-dominating function (R2F) is a function $f:V\rightarrow \{0,1,2\}$ with the property that for every vertex $v\in V$ with $f(v)=0$ there is a neighbor $u$ of $v$ with $f(u)=2$, or there are two neighbors $x,y$ of $v$ with $f(x)=f(y)=1$. A total Roman $\{2\}$-dominating function (TR2DF) is an R2F $f$ such that the set of vertices with $f ...
Hossein Abdollahzadeh Ahangar +3 more
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Roman {2}-domination in Graphs and Graph Products
Iranian Journal of Mathematical Sciences and Informatics, 2023 9 pages, 2 ...
Alizadeh, F. +3 more
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New complexity results on Roman {2}-domination
RAIRO - Operations Research, 2023 The study of a variant of Roman domination was initiated by Chellali et al. [Discrete Appl. Math. 204 (2016) 22–28]. Given a graph G with vertex set V, a Roman {2}-dominating function f : V → {0, 1, 2} has the property that for every vertex v ∈ V with f(v) = 0, either there exists a vertex u adjacent to v with f(u) = 2, or at least two vertices x, y ...
Leoni, Valeria Alejandra +1 more
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Total Roman {2}-domination in graphs [PDF]
Quaestiones Mathematicae, 2019 Given a graph $G=(V,E)$, a function $f:V\rightarrow \{0,1,2\}$ is a total Roman $\{2\}$-dominating function if: (1) every vertex $v\in V$ for which $f(v)=0$ satisfies that $\sum_{u\in N(v)}f(u)\geq 2$, where $N(v)$ represents the open neighborhood of $v$, and (2) every vertex $x\in V$ for which $f(x)\geq 1$ is adjacent to at least one vertex $y\in V ...
Suitberto Cabrera García +3 more
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Roman \{2\} -domination problem in graphs
Discussiones Mathematicae Graph Theory, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen Hangdi, Lu Changhong
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A characterization of trees with equal Roman 2-domination and Roman domination numbers
Communications in Combinatorics and Optimization, 2019 Summary: Given a graph \(G=(V,E)\) and a vertex \(v \in V\), by \(N(v)\) we represent the open neighbourhood of \(v\). Let \(f:V\rightarrow \{0,1,2\}\) be a function on \(G\). The weight of \(f\) is \(\omega(f)=\sum_{v\in V}f(v)\) and let \(V_i=\{v\in V :f(v)=i\}\), for \(i=0,1,2\).
Gonzalez Yero, Ismael +1 more
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The 2-domination and Roman domination numbers of grid graphs
Discrete Mathematics & Theoretical Computer Science, 2019 We investigate the 2-domination number for grid graphs, that is the size of a smallest set $D$ of vertices of the grid such that each vertex of the grid belongs to $D$ or has at least two neighbours in $D$. We give a closed formula giving the 2-domination number of any $n \!\times\! m$ grid, hereby confirming the results found by Lu and Xu, and Shaheen
Rao, Michaël, Talon, Alexandre
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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
Discussiones Mathematicae Graph Theory, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abolfazl Poureidi, Nader Jafari Rad
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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