Results 1 to 10 of about 708,201 (190)
Double Roman Domination: A Survey
Mathematics, 2023 Since 2016, when the first paper of the double Roman domination appeared, the topic has received considerable attention in the literature. We survey known results on double Roman domination and some variations of the double Roman domination, and a list ...
Janez Žerovnik +2 more
exaly +5 more sources
Varieties of Roman domination II [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 In this work, we continue to survey what has been done on the Roman domination. More precisely, we will present in two sections several variations of Roman dominating functions as well as the signed version of some of these functions.
Mustapha Chellali +2 more
exaly +5 more sources
Complexity of Roman {2}-domination and the double Roman domination in graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 For a simple, undirected graph a Roman {2}-dominating function (R2DF) has the property that for every vertex with f(v) = 0, either there exists a vertex with f(u) = 2, or at least two vertices with The weight of an R2DF is the sum The minimum weight of ...
Chakradhar Padamutham
exaly +3 more sources
Relating 2-Rainbow Domination To Roman Domination
Discussiones Mathematicae Graph Theory, 2017 For a graph G, let R(G) and yr2(G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G) ≤ R(G) ≤ 3/2yr2(G). Fujita and Furuya [Difference between 2-rainbow domination and Roman domination
Alvarado José D. +2 more
doaj +6 more sources
Independent roman $\{3\}$-domination [PDF]
Transactions on Combinatorics, 2022 Let $G$ be a simple, undirected graph. In this paper, we initiate the study of independent Roman $\{3\}$-domination. A function $g : V(G) \rightarrow \lbrace 0, 1, 2, 3 \rbrace$ having the property that $\sum_{v \in N_G(u)}^{} g(v) \geq 3$, if $g(u) = 0$,
P. Chakradhar, P. Venkata Subba Reddy
doaj +2 more sources
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
TERESA Haynes, Stephen T Hedetniemi
exaly +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.
M. Cera +2 more
semanticscholar +4 more sources
On The Roman Domination Stable Graphs
Discussiones Mathematicae Graph Theory, 2017 A Roman dominating function (or just 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.
Hajian Majid, Rad Nader Jafari
doaj +2 more sources
Varieties of Roman domination IV
AKCE International Journal of Graphs and CombinatoricsRoman domination was introduced in 2004 by Cockayne, Dreyer, Hedetniemi, and Hedetniemi. If [Formula: see text] is the vertex set of a graph G, then a function [Formula: see text] is a Roman dominating function if every vertex [Formula: see text] for ...
M. Chellali +3 more
doaj +2 more sources
A characterization of trees with equal Roman $\{2\}$-domination and Roman domination numbers [PDF]
Communications in Combinatorics and Optimization, 2019 Given a graph $G=(V,E)$ and a vertex $v \in V$, by $N(v)$ we represent the open neighbourhood of $v$. Let $f:V\rightarrow \{0,1,2\}$ be a function on $G$. The weight of $f$ is $\omega(f)=\sum_{v\in V}f(v)$ and let $V_i=\{v\in V \colon f(v)=i\}$, for $i=0,
Abel Cabrera Martinez, Ismael G. Yero
doaj +3 more sources