Results 151 to 160 of about 1,279 (174)

Outer independent Roman dominating functions in graphs

International Journal of Computer Mathematics, 2017
ABSTRACTA Roman dominating function (RDF) on a graph G is a function f:V(G)→{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. A function f:V(G)→{0,1,2} is an outer-independent Roman dominating function (OIRDF) on G if f is an RDF and V0 is an independent set.
Mustapha Chellali, Vladimir Samodivkin, Hossein Abdollahzadeh Ahangar   +2 more
exaly   +2 more sources

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 ...
Dorota Kuziak, Ismael G Yero, Iztok Peterin   +2 more
exaly   +3 more sources

Algorithmic Results in Roman Dominating Functions on Graphs

SSRN Electronic Journal, 2022
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Abolfazl Poureidi, Jafar Fathali
openaire   +2 more sources

Perfect Roman domination in trees [PDF]

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
Gary Macgillivray, Michael Henning
exaly   +2 more sources

Trees with unique Roman dominating functions of minimum weight

Discrete Mathematics, Algorithms and Applications, 2014
A Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2} satisfying the condition that every vertex u of G for which f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2. The weight of a Roman dominating function is the value f(V(G)) = ∑u∈V(G)f(u).
Mustapha Chellali, Nader Jafari Rad
openaire   +1 more source

Algorithmic complexity of triple Roman dominating functions on graphs

2023
Summary: Given a graph \(G=(V,E)\), a function \(f:V\to \{0,1,2,3,4\}\) is a triple Roman dominating function (TRDF) of \(G\), for each vertex \(v\in V\), (i) if \(f (v) = 0 \), then \(v\) must have either one neighbour in \(V_4\), or either two neighbours in \(V_2 \cup V_3\) (one neighbour in \(V_3)\) or either three neighbours in \(V_2\), (ii) if \(f
Poureidi, Abolfazl, Fathali, Jafar
openaire   +1 more source

The Roman domatic number of a graph [PDF]

Applied Mathematics Letters, 2010
A Roman dominating function on a graph G is a labeling f:V(G)⟶{0,1,2} such that every vertex with label 0 has a neighbor with label 2. A set {f1,f2,…,fd} of Roman dominating functions on G with the property that ∑i=1dfi(v)≤2 for each v∈V(G) is called a ...
Lutz Volkmann, S M Sheikholeslami
exaly   +2 more sources

Enhancing Network Security in Distributed Systems Using Middle Roman Dominating Functions

Communications on Applied Nonlinear Analysis
A Middle Roman dominating function (MRDN) on a graph G = (V,E) is a function f:v→{0,1,2,3} satisfying the condition that every vertex u with f(u)=0 is adjacent to at most one vertex v with f(v)=2 or 3. Further if a vertex is assigned 2, then at most two of its vertices can be assigned 0 and if a vertex is assigned 3, then all its neighbours can be ...
openaire   +1 more source

Algorithmic results in Roman dominating functions on graphs

Information Processing Letters, 2023
Abolfazl Poureidi, Jafar Fathali
exaly  

Nearly tight approximation algorithm for (connected) Roman dominating set

Optimization Letters, 2022
Ding-Zhu Du, Zhao Zhang, Yingli Ran
exaly