Results 21 to 30 of about 10,626,776 (155)
Double Roman and double Italian domination [PDF]
, 2023 Let $G$ be a graph with vertex set $V(G)$. A double Roman dominating function (DRDF) on a graph $G$ is a function \( f:V(G)\longrightarrow\{0,1,2,3\} \) that satisfies the following conditions: (i) If $f(v)=0$, then $v$ must have a neighbor $w$ with $f(w)
Volkmann, Lutz, Lutz Volkmann
core +1 more source
A note on the double Roman domination number of graphs [PDF]
, 2020 summary:For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarrow \{0,1,2,3\}$ 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 with $f(w)
Chen, Xue-Gang
core +1 more source
Bounds on signed total double Roman domination [PDF]
Communications in Combinatorics and Optimization, 2020 A signed total double Roman dominating function (STDRDF) on {an} isolated-free graph $G=(V,E)$ is a function $f:V(G)\rightarrow\{-1,1,2,3\}$ such that (i) every vertex $v$ with $f(v)=-1$ has at least two neighbors assigned 2 under $f$ or one neighbor ...
L. Shahbazi +3 more
doaj +1 more source
Further results on independent double roman trees
AKCE International Journal of Graphs and Combinatorics, 2022 A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v
A. Rahmouni +3 more
doaj +1 more source
On the Roman Edge Domination Number of a Graph [PDF]
, 2010 Let G be a simple graph with vertex set V (G) and edge set E(G)
K. Ebadi +5 more
core +1 more source
On the Outer-Independent Double Roman Domination of Graphs
Frontiers in Applied Mathematics and Statistics, 2021 An outer-independent double Roman dominating function (OIDRDF) of a graph G is a function h:V(G)→{0,1,2,3} such that i) every vertex v with f(v)=0 is adjacent to at least one vertex with label 3 or to at least two vertices with label 2, ii) every vertex ...
Yongsheng Rao +4 more
doaj +1 more source
On Roman, Global and Restrained Domination in Graphs [PDF]
, 2010 In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible.
Zverovich, Vadim +3 more
core +1 more source
Double Roman Graphs in P(3k, k)
Mathematics, 2021 A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3} with the properties that if f(u)=0, then vertex u is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and if f(u)=1, then vertex u is ...
Zehui Shao +5 more
doaj +1 more source
On the double Roman domination number in oriented trees
, 2023 Abstract Note: Please see pdf for full abstract with equations. Let D = (V,A) be a digraph. A double Roman dominating function on a digraph D is a function ƒ :V → {0, 1, 2, 3} such that every vertex u for which ƒ(u) = 0 has an in-neighbor v for which ƒ(v) = 3 or at least two in-neighbors assigned 2 under ƒ, while if ƒ(u) = 1, then the vertex u ...
Lyes Ouldrabah +2 more
openaire +1 more source
Perfect double Italian domination of a graph
AKCE International Journal of Graphs and Combinatorics, 2023 For a graph [Formula: see text] with [Formula: see text] and [Formula: see text], a perfect double Italian dominating function is a function [Formula: see text] having the property that [Formula: see text], for every vertex [Formula: see text] with ...
Guoliang Hao +2 more
doaj +1 more source