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Total Roman {2}-Dominating Functions in Graphs
Discussiones Mathematicae Graph Theory, 2022 A Roman {2}-dominating function (R2F) is a function f : V → {0, 1, 2} with the property that for every vertex v ∈ 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.
Ahangar H. Abdollahzadeh +3 more
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Strong Equality of Perfect Roman and Weak Roman Domination in Trees [PDF]
Mathematics, 2019 Let G = ( V , E ) be a graph and f : V ⟶ { 0 , 1 , 2 } be a function. Given a vertex u with f ( u ) = 0 , if all neighbors of u have zero weights, then u is called undefended with respect to f. Furthermore, if every vertex u with
Abdollah Alhevaz +3 more
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Dominating the Direct Product of Two Graphs through Total Roman Strategies [PDF]
Mathematics, 2020 Given a graphGwithout isolated vertices, a total Roman dominating function forGis a function f:V(G)->{0,1,2}such that every vertexuwithf(u)=0is adjacent to a vertexvwithf(v)=2, and the set of vertices with positive labels induces a graph of minimum ...
Abel Cabrera Martinez +2 more
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A note on the edge Roman domination in trees [PDF]
Electronic Journal of Graph Theory and Applications, 2017 A subset $X$ of edges of a graph $G$ is called an \textit{edgedominating set} of $G$ if every edge not in $X$ is adjacent tosome edge in $X$. The edge domination number $\gamma'(G)$ of $G$ is the minimum cardinality taken over all edge dominating sets of
Nader Jafari Rad
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Bounds on the restrained Roman domination number of a graph
Communications in Combinatorics and Optimization, 2016 A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) =2$.
H. Abdollahzadeh Ahangar +1 more
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Double Roman domination and domatic numbers of graphs [PDF]
Communications in Combinatorics and Optimization, 2018 A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in \cite{bhh} as a function $f:V(G)\rightarrow\{0,1,2,3\}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least two neighbors assigned 2 ...
L. Volkmann
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A note on k-Roman graphs [PDF]
Opuscula Mathematica, 2013 Let \(G=\left(V,E\right)\) be a graph and let \(k\) be a positive integer. A subset \(D\) of \(V\left( G\right) \) is a \(k\)-dominating set of \(G\) if every vertex in \(V\left( G\right) \backslash D\) has at least \(k\) neighbours in \(D\).
Ahmed Bouchou +2 more
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Some Properties of Double Roman Domination
Discrete Dynamics in Nature and Society, 2020 A double Roman dominating function on a graph G is a function f:VG⟶0,1,2,3 satisfying the conditions that every vertex u for which fu=0 is adjacent to at least one vertex v for which fv=3 or two vertices v1 and v2 for which fv1=fv2=2 and every vertex u ...
Hong Yang, Xiaoqing Zhou
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Perfect Roman domination in trees
Discrete Applied Mathematics, 2018 A perfect Roman dominating function on a graph G is a function f:V(G)→{0,1,2} satisfying the condition that every vertex u with f(u)=0 is adjacent to exactly one vertex v for which f(v)=2. The weight of a perfect Roman dominating function f is the sum of
Michael A Henning +2 more
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Restrained roman domination in graphs [PDF]
Transactions on Combinatorics, 2015 A Roman dominating function (RDF) on a graph G = (V,E) is defined to be a function 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. A set S V is a Restrained dominating set if every
Roushini Leely Pushpam +1 more
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