Results 11 to 20 of about 820 (190)
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 an R2DF is called the Roman {2}-domination number and is denoted by A double Roman dominating ...
Chakradhar Padamutham +1 more
exaly +6 more sources
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
openaire +3 more sources
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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A Borane Sandwich Analogue of Ferrocene
Angewandte Chemie, EarlyView.The first ferrocene analogue with two boron‐based ligands is identified through a global exploration of the FeB10H20 potential energy surface. The η5,η5‐Fe(B5H10)2 complex emerges as the global minimum, showing that metal coordination inverts borane stability and enables aromatic boron rings inaccessible in isolation.
Viviana Roman‐Ventura +8 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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