Results 11 to 20 of about 152,920 (311)
Critical graphs with Roman domination number four [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 A Roman domination function on a graph G is a function satisfying the condition that every vertex u for which r(u) = 0 is adjacent to at least one vertex v for which r(v) = 2. The weight of a Roman domination function is the value The Roman domination number of G is the minimum weight of a Roman domination function on G.
A. Martínez-Pérez, D. Oliveros
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Triple Roman domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2022 For a graph $G=(V, E)$, a triple Roman domination function is a function $f: V(G)\longrightarrow\{0, 1, 2, 3, 4\}$ having the property that for any vertex $v\in V(G)$, if $f(v)<3$, then $f(\mbox{AN}[v])\geq|\mbox{AN}(v)|+3$, where $\mbox{AN}(v)=\{w\in N(v)\mid f(w)\geq1\}$ and $\mbox{AN}[v]=\mbox{AN}(v)\cup\{v\}$.
Amjadi, J., Sadeghi, H.
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Bounds on the locating Roman dominating number in trees
Discussiones Mathematicae Graph Theory, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jafari Rad Nader, Rahbani Hadi
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The distance Roman domination numbers of graphs
Discussiones Mathematicae Graph Theory, 2013 Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k from each other. The weight of a k-distance Roman dominating function f is the value w(f) =∑v∈V f(v).
H. Aram +3 more
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On the Quasi-Total Roman Domination Number of Graphs
Mathematics, 2021 Domination theory is a well-established topic in graph theory, as well as one of the most active research areas. Interest in this area is partly explained by its diversity of applications to real-world problems, such as facility location problems ...
Abel Cabrera Martínez +2 more
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On the strong Roman domination number of graphs
Discrete Applied Mathematics, 2017 Based on the history that the Emperor Constantine decreed that any undefended place (with no legions) of the Roman Empire must be protected by a "stronger" neighbor place (having two legions), a graph theoretical model called Roman domination in graphs was described. A Roman dominating function for a graph $G=(V,E)$, is a function $f:V\rightarrow \{0,1,
M.P. Álvarez-Ruiz +4 more
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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 $f\colon V(G)\to \{0,1,2\}$ such that if $f(v)=0$ then, the vertex $v$ is adjacent to at least one vertex $w$
J. A. Martínez +2 more
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Graphs with large hop Roman domination number [PDF]
Computer Science Journal of Moldova, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shabani, E. +2 more
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An Upper Bound for the Eternal Roman Domination Number
MathematicsImagine using mobile guards to defend the vertices of a graph G from a sequence of attacks subject to the conditions that after each attack: (i) each guard either remains in place or moves to an adjacent vertex; (ii) the configuration of guards forms a ...
R. Brewster +2 more
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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 ...
A. Cabrera Martínez +3 more
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