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Discrete Applied Mathematics, 2016 For a graph G=(V,E), a double Roman dominating function is a function f:V→{0,1,2,3} having the property that if f(v)=0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor with f(w)=3, and if f(v)=1, then vertex v must have ...
Teresa W. Haynes, Stephen Hedetniemi
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On the Double Roman Domination in Graphs [PDF]
Discrete Applied Mathematics, 2017 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)
Mustapha Chellali +2 more
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Maximal double Roman domination in graphs [PDF]
Applied Mathematics and Computation, 2022 A maximal double Roman dominating function (MDRDF) on a graph $G=(V,E)$ is a function $f:V(G)\rightarrow \{0,1,2,3\}$ such that \textrm{(i) }every vertex $v$ with $f(v)=0$ is adjacent to least two vertices { assigned $2$ or to at least one vertex ...
H. A. Ahangar +3 more
semanticscholar +4 more sources
Restrained double Roman domination of a graph [PDF]
RAIRO - Operations Research, 2021 For a graph $G=(V,E)$, a restrained double Roman dominating function is a function $f:V\rightarrow\{0,1,2,3\}$ 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 $w$ with $f(
D. Mojdeh, Iman Masoumi, L. Volkmann
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Some Properties of Double Roman Domination [PDF]
Discrete Dynamics in Nature and Society, 2020 A double Roman dominating function on a graph G is a function f:VG⟶0,1,2,3 satisfying the conditions that every vertex u for which fu=0 is adjacent to at least one vertex v for which fv=3 or two vertices v1 and v2 for which fv1=fv2=2 and every vertex u ...
Hong Yang, Xiaoqing Zhou
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Signed double Roman domination on cubic graphs [PDF]
Applied Mathematics and Computation, 2023 The signed double Roman domination problem is a combinatorial optimization problem on a graph asking to assign a label from $\{\pm{}1,2,3\}$ to each vertex feasibly, such that the total sum of assigned labels is minimized.
Enrico Iurlano +3 more
semanticscholar +10 more sources
Double Roman and double Italian domination [PDF]
Discussiones Mathematicae Graph Theory, 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)
Lutz Volkmann
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Upper Bounds for Double Roman Domination and [k]-Roman Domination of Cylindrical Graphs Cm☐Pn [PDF]
AxiomsRoman-type domination parameters form an important class of graph invariants that model protection and resource allocation problems on networks. Among them, [k]-Roman domination provides a unified framework that generalizes Roman, double Roman, and ...
Simon Brezovnik, Janez Žerovnik
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The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2)
Mathematics, 2018 A double Roman dominating function (DRDF) f on a given graph G is a mapping from V ( G ) to { 0 , 1 , 2 , 3 } in such a way that a vertex u for which f ( u ) = 0 has at least a neighbor labeled 3 or two neighbors both labeled 2 ...
Huiqin Jiang +4 more
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Discharging Approach for Double Roman Domination in Graphs
IEEE Access, 2018 The discharging method is most well-known for its central role in the proof of the Four Color Theorem. This proof technique was extensively applied to study various graph coloring problems, in particular on planar graphs.
Zehui Shao +5 more
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