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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
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[k]-Roman Domination in Digraphs [PDF]
, 2023 Let D=(V(D),A(D)) be a finite, simple digraph and k a positive integer. A function f:V(D)→{0,1,2,…,k+1} is called a [k]-Roman dominating function (for short, [k]-RDF) if f(AN−[v])≥|AN−(v)|+k for any vertex v∈V(D), where AN&
Ruijuan Li, Xinhong Zhang, Xin Song
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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
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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
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Restrained condition on double Roman dominating functions [PDF]
, 2022 We continue the study of restrained double Roman domination in graphs. For a graph $G=\big{(}V(G),E(G)\big{)}$, a double Roman dominating function $f$ is called a restrained double Roman dominating function (RDRD function) if the subgraph induced by $\{v\
Samadi, Babak +12 more
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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
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Double domination in lexicographic product graphs [PDF]
, 2020 [EN] In a graph G, a vertex dominates itself and its neighbours. A subset S subset of V(G) is said to be a double dominating set of G if S dominates every vertex of G at least twice.
Cabrera Martínez, Abel +3 more
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On the Outer Independent Total Double Roman Domination in Graphs [PDF]
, 2023 A double Roman dominating function (DRDF) on a graph G=(V, E) is a function f:V→ {0,1,2,3} satisfying (i) if f(v)=0, then there must be at least two neighbors assigned 2 under f or one neighbor w with f(w)=3; and (ii) if f(v)=1 then v must be adjacent to
H. Abdollahzadeh Ahangar +7 more
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On the domination of triangulated discs [PDF]
, 2023 summary:Let $G$ be a $3$-connected triangulated disc of order $n$ with the boundary cycle $C$ of the outer face of $G$. Tokunaga (2013) conjectured that $G$ has a dominating set of cardinality at most $\frac 14(n+2)$.
Abd Aziz, Noor A'lawiah +2 more
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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
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