Results 71 to 80 of about 1,605,758 (310)

Roman Domination in Complementary Prisms [PDF]

, 2017
The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect match- ing between the corresponding vertices of G and G.
Alhashim, Alawi I
core   +3 more sources

Graphs with Large Vertex–Edge Roman {2}-Domination Number

Mathematics
For a graph G=(V,E), a function f:V⟶{0,1,2} is a vertex–edge Roman {2}-dominating function (veR2DF) if for every edge xy∈E, either f(x)+f(y)≥1 or ∑z∈N(x)∪N(y)f(z)≥2. The sum ∑v∈Vf(v) is the weight of the function f.
Ahlam Almulhim
doaj   +1 more source

Global Roman domination in graphs

Discrete Applied Mathematics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
P. Roushini Leely Pushpam, Padmapriea Sampath   +1 more
openaire   +2 more sources

Powers of Large Matrices on GPU Platforms to Compute the Roman Domination Number of Cylindrical Graphs [PDF]

IEEE Access
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 $w$
José Antonio Martínez, Ester M. Garzón, M. L. Puertas   +2 more
semanticscholar   +1 more source

Roman {2}-Domination

, 2016
In this paper, we initiate the study of a variant of Roman dominating functions. For a graph G=(V,E), a Roman {2}-dominating function f:V→{0,1,2} has the property that for every vertex v∈V with f(v)=0, either v is adjacent to a vertex assigned 2 under f,
Haynes, Teresa W., Chellali, Mustapha, Hedetniemi, Stephen T., McRae, Alice A.   +3 more
core   +1 more source

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 ...
Aram Hamideh, Norouzian Sepideh, Sheikholeslami Seyed Mahmoud   +2 more
doaj   +1 more source

Restrained double Roman domination of a graph

, 2022
For a graph G = (V, E), a restrained double Roman dominating function is a function f : V → {0, 1, 2, 3} having the property that if f(v) = 0, then the vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(
Doost Ali Mojdeh, Iman Masoumi, Lutz Volkmann   +2 more
core   +1 more source

On a generalization of Roman domination with more legions

, 2022
In this note, we generalize the concepts of (perfect) Roman and Italian dominations to (perfect) strong Roman and Roman k-domination for arbitrary positive integer k. These generalizations cover some of previous ones.
Ghasr, Fahimeh Khosh-Ahang
core  

Total Perfect Roman Domination

, 2023
A total perfect Roman dominating function (TPRDF) on a graph G=(V,E) is a function f from V to {0,1,2} satisfying (i) every vertex v with f(v)=0 is a neighbor of exactly one vertex u with f(u)=2; in addition, (ii) the subgraph of G that is induced by the
Ahlam Almulhim
core   +1 more source

Weak signed Roman k-domination in digraphs [PDF]

Opuscula Mathematica
Let \(k\geq 1\) be an integer, and let \(D\) be a finite and simple digraph with vertex set \(V(D)\). A weak signed Roman \(k\)-dominating function (WSRkDF) on a digraph \(D\) is a function \(f \colon V(D)\rightarrow \{-1,1,2\}\) satisfying the condition
Lutz Volkmann
doaj   +1 more source