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Further Results on the [k]-Roman Domination in Graphs [PDF]
Bulletin of the Iranian Mathematical SocietyIn 2016, Beeler et al. defined the double Roman domination as a variation of Roman domination. Sometime later, in 2021, Ahangar et al. introduced the concept of [k]- Roman domination in graphs and settled some results on the triple Roman domination ...
J.C. Valenzuela +3 more
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Several Roman domination graph invariants on Kneser graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 This paper considers the following three Roman domination graph invariants on Kneser graphs: Roman domination, total Roman domination, and signed Roman domination.
Tatjana Zec, Milana Grbić
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On [k] -Roman domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 For an integer [Formula: see text] let f be a function that assigns labels from the set [Formula: see text] to the vertices of a simple graph [Formula: see text].
N. Khalili +3 more
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Relating 2-Rainbow Domination To Roman Domination
Discussiones Mathematicae Graph Theory, 2017 For a graph G, let R(G) and yr2(G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G) ≤ R(G) ≤ 3/2yr2(G). Fujita and Furuya [Difference between 2-rainbow domination and Roman domination
Alvarado José D. +2 more
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Restrained double Roman domination of a graph [PDF]
RAIRO - Operations Research, 2022 For a graph G = (V, E), a restrained double Roman dominating function is a function f : V → {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 w with f(w) = 3, and if f(v) = 1, then the vertex v must have at least one neighbor w with f(w) ≥ 2, and at the same time ...
Doost Ali Mojdeh +2 more
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Weak signed Roman domination in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 A weak signed Roman dominating function (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as a function $f:V(G)\rightarrow\{-1,1,2\}$ having the property that $\sum_{x\in N[v]}f(x)\ge 1$ for each $v\in V(G)$, where $N[v]$ is the closed ...
Lutz Volkmann
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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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Powers of Large Matrices on GPU Platforms to Compute the Roman Domination Number of Cylindrical Graphs [PDF]
IEEE Access, 2021 The Roman domination in a graph G is a variant of the classical domination, defined by means of a so-called Roman domination function f : V (G) - {0, 1, 2} such that if f (v) = 0 then, the vertex v is adjacent to at least one vertex w with f (w) = 2. The
J. A. Martinez +2 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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Perfect Roman domination in middle graphs [PDF]
Discrete Mathematics Letters, 2021 The middle graph $M(G)$ of a graph $G$ is the graph obtained by subdividing each edge of $G$ exactly once and joining all these newly introduced vertices of adjacent edges of $G$. A perfect Roman dominating function on a graph $G$ is a function $f : V(G) \rightarrow \{0, 1, 2\}$ satisfying the condition that every vertex $v$ with $f(v)=0$ is adjacent ...
Kijung Kim
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