Results 11 to 20 of about 862,623 (267)
Survey on Roman {2}-Domination
MathematicsThe notion of Roman {2}-domination was introduced in 2016 as a variant of Roman domination, a concept inspired by a defending strategy used by the emperor Constantine (272–337 AD) to protect the Roman Empire.
Bana Al Subaiei +2 more
exaly +4 more sources
On the double Roman domination in graphs [PDF]
Discrete Applied Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hossein Abdollahzadeh Ahangar +1 more
exaly +5 more sources
Perfect Domination, Roman Domination and Perfect Roman Domination in Lexicographic Product Graphs
Fundamenta Informaticae, 2022 The aim of this paper is to obtain closed formulas for the perfect domination number, the Roman domination number and the perfect Roman domination number of lexicographic product graphs. We show that these formulas can be obtained relatively easily for the case of the first two parameters.
Abel Cabrera Martínez +2 more
core +5 more sources
Anarchism and non-domination [PDF]
, 2019 In this article we recover the classical anarchist deployment of republican tropes of non-domination, tyranny and slavery, to expose the conservative limits of the contemporary neo-Roman republican revival. For the anarchists, the modern nation state and
WAL Prichard (21872402) +1 more
core +16 more sources
Perfect Roman Domination and Unique Response Roman Domination [PDF]
CoRR, 2023 The idea of enumeration algorithms with polynomial delay is to polynomially bound the running time between any two subsequent solutions output by the enumeration algorithm. While it is open for more than four decades if all minimal dominating sets of a graph can be enumerated in output-polynomial time, it has recently been proven that pointwise-minimal
Henning Fernau, Kevin Mann
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Roman domination in graphs [PDF]
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
openaire +3 more sources
Roman Domination in Weighted Graphs
MathematicsA Roman dominating function for a (non-weighted) graph G=(V,E) is a function f:V→{0,1,2} such that every vertex u∈V with f(u)=0 has at least one neighbor v∈V such that f(v)=2. The minimum weight ∑v∈Vf(v) of a Roman dominating function f on G is called the Roman domination number of G and is denoted by γR(G).
Martín Cera +2 more
openaire +4 more sources
[k]-Roman Domination in Digraphs
Symmetry, 2023 Let D=(V(D),A(D)) be a finite, simple digraph and k a positive integer. A function f:V(D)→{0,1,2,…,k+1} is called a [k]-Roman dominating function (for short, [k]-RDF) if f(AN−[v])≥|AN−(v)|+k for any vertex v∈V(D), where AN−(v)={u∈N−(v):f(u)≥1} and AN−[v]=AN−(v)∪{v}. The weight of a [k]-RDF f is ω(f)=∑v∈V(D)f(v).
Xinhong Zhang, Xin Song, Ruijuan Li
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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
doaj +2 more sources
Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees
Discussiones Mathematicae Graph Theory, 2013 A Roman dominating function (RDF) on a graph G = (V,E) is a function f : V −→ {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.
Chellali Mustapha, Rad Nader Jafari
doaj +2 more sources