Results 21 to 30 of about 129,618 (274)
Bounds on signed total double Roman domination [PDF]
Communications in Combinatorics and Optimization, 2020 A signed total double Roman dominating function (STDRDF) on {an} isolated-free graph $G=(V,E)$ is a function $f:V(G)\rightarrow\{-1,1,2,3\}$ such that (i) every vertex $v$ with $f(v)=-1$ has at least two neighbors assigned 2 under $f$ or one neighbor ...
L. Shahbazi +3 more
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Further Results on the Total Roman Domination in Graphs
Mathematics, 2020 Let G be a graph without isolated vertices. A function f : V ( G ) → { 0 , 1 , 2 } is a total Roman dominating function on G if every vertex v ∈ V ( G ) for which f ( v ) = 0 is adjacent to at least one vertex u ...
Abel Cabrera Martínez +2 more
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On the total Roman domination stability in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 A total Roman dominating function on a graph G is a function satisfying the conditions: (i) every vertex u with f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2; (ii) the subgraph induced by the vertices assigned non-zero values has ...
Ghazale Asemian +3 more
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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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Critical graphs with Roman domination number four
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.
A. Martínez-Pérez, D. Oliveros
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On trees with equal Roman domination and outer-independent Roman domination number [PDF]
Communications in Combinatorics and Optimization, 2019 A Roman dominating function (RDF) on a graph $G$ is a function $f : V (G) \to \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$.
S. Nazari-Moghaddam, S.M. Sheikholeslami
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Discrete Mathematics, 2004 The paper studies the Roman domination in graphs. It is a special kind of domination whose introduction was motivated by military rules of the ancient Roman Empire. Let \(G\) be a graph with vertex set \(V(G)\), and let \(f: V(G)\to \{0,1,2\}\). If to each vertex \(v\) with \(f(v)= 0\) there exists a vertex \(w\) with \(f(w)= 2\) adjacent to \(v ...
Ernest J. Cockayne +3 more
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What Has Athens to Do with Rome? Tocqueville and the New Republicanism [PDF]
, 2017 The recent debate over “republican” conceptions of freedom as non-domination has re- invigorated philosophical discussions of freedom. However, “neo-Roman” republicanism, which has been characterized as republicanism that respects equality, has largely ...
Jech, Alexander
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Vertex-Edge Roman Domination [PDF]
Kragujevac Journal of Mathematics, 2021 A vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V,E) is a function f : V (G) →{0, 1, 2} such that for each edge e = uv either max{f(u),f(v)}≠0 or there exists a vertex w such that either wu ∈ E or wv ∈ E and f(w) = 2. The weight of a ve-RDF is the sum of its function values over all vertices.
Kumar, H. Naresh, Venkatakrishnan, Y. B.
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Coloring, location and domination of corona graphs [PDF]
, 2012 A vertex coloring of a graph $G$ is an assignment of colors to the vertices of $G$ such that every two adjacent vertices of $G$ have different colors. A coloring related property of a graphs is also an assignment of colors or labels to the vertices of a ...
Aguilar, A. Rondón +2 more
core +4 more sources