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Double Roman domination and domatic numbers of graphs [PDF]
, 2018 A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in \cite{bhh} as a function $f:V(G)\rightarrow\{0,1,2,3\}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least two neighbors assigned 2 ...
L. Volkmann
core +1 more source
Signed double Roman k-domination in digraphs
Let D be a finite simple digraph with vertex set V(D), and let k≥1 be an integer. A signed double Roman k-dominating function (SDRkDF) on a digraph D is a function f: V(D) → {-1,1,2,3} satisfying certain conditions.
Zverovich, Vadim, Volkmann, Lutz
core
Some Bounds on the Double Domination of Signed Generalized Petersen Graphs and Signed I-Graphs [PDF]
, 2019 In a graph $G$, a vertex dominates itself and its neighbors. A subset $D \subseteq V(G)$ is a double dominating set of $G$ if $D$ dominates every vertex of $G$ at least twice.
Sehrawat, Deepak, Bhattacharjya, Bikash
core +1 more source
On the signed Roman edge $k$-domination in graphs
, 2017 Let $k\geq 1$ be an integer, and $G=(V,E)$ be a finite and simple graph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph $G$ is the set consisting of $e$ and all edges having a common end-vertex with $e$. A signed Roman edge $k$-
A. Mahmoodi
core +1 more source
The restrained double Roman domination and graph operations
A restrained double Roman dominating function (RDRD-function) on a graph G is a function f:V(G)→{0, 1, 2, 3} that satisfies two conditions: (1) If f(v)
Yue, Jun, Gao, Zhipeng, Xi, Changqing
core +3 more sources
Bounds for signed double Roman k-domination in trees
RAIRO - Operations Research, 2019 Let k ≥ 1 be an integer and G be a simple and finite graph with vertex set V(G). A signed double Roman k-dominating function (SDRkDF) on a graph G is a function f:V(G) → {−1,1,2,3} such that (i) every vertex v with f(v) = −1 is adjacent to at least two vertices assigned a 2 or to at least one vertex w with f(w) = 3, (ii) every vertex v with f(v) = 1 is
Hong Yang +6 more
openaire +2 more sources
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, Darja Rupnik Poklukar
exaly +2 more sources