Results 251 to 260 of about 1,370 (272)

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.
Hossein Abdollahzadeh Ahangar, Mustapha Chellali, Vladimir Samodivkin   +2 more
exaly   +2 more sources

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

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 results in Roman dominating functions on graphs

Information Processing Letters, 2023
Abolfazl Poureidi, Jafar Fathali
exaly  

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

Nearly tight approximation algorithm for (connected) Roman dominating set

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

Restrained condition on double Roman dominating functions

Applied Mathematics and Computation, 2023
Mustapha Chellali, Doost Ali Mojdeh, S M Sheikholeslami   +2 more
exaly  

Outer-Independent Signed Roman Domination Function in Graphs

Operations Research Forum
Ning Li, Peng Li, Jianhui Shang
openaire   +1 more source

Signed Total Roman Dominating Functions of Corona Product of a Path with a Complete Graph

International Journal of Mathematics Trends and Technology, 2017
C. Shobha Rani, S. Jeelani Begum, G.S.S Raju, S.Gouse Mohiddin   +3 more
openaire   +1 more source

On the signed Roman k-domination in graphs

Quaestiones Mathematicae, 2020
S M Sheikholeslami, Lutz Volkmann
exaly