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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
On the Outer Independent Double Roman Domination Number [PDF]
Bulletin of the Iranian Mathematical Society, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Doost Ali Mojdeh +3 more
exaly +5 more sources
Independent Roman Domination: The Complexity and Linear-Time Algorithm for Trees
Symmetry, 2022 For a graph G=(V,E), an independent Roman dominating function (IRDF) is a function f:V→{0,1,2} having the property that: (1) every vertex assigned a value of 0 is adjacent to at least one vertex assigned a value of 2, (2) there are no two adjacent ...
Zhixing Duan +4 more
semanticscholar +3 more sources
Independent Double Roman Domination in Graphs
Bulletin of the Iranian Mathematical Society, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maimani, Hamidreza +4 more
exaly +5 more sources
On trees with equal Roman domination and outer-independent Roman domination numbers
Communications in Combinatorics and Optimization, 2019 Summary: A Roman dominating function (RDF) on a graph \(G\) is a function \(f : V (G) \to \{0, 1, 2\}\) satisfying the condition that every vertex \(u\) for which \(f(u) = 0\) is adjacent to at least one vertex \(v\) for which \(f(v) = 2\). A Roman dominating function \(f\) is called an outer-independent Roman dominating function (OIRDF) on \(G\) if ...
Sheikholeslami, Seyed Mahmoud +1 more
openaire +3 more sources
An improved upper bound on the independent double Roman domination number of trees
AKCE International Journal of Graphs and Combinatorics, 2022 For a graph [Formula: see text] an independent double Roman dominating function (IDRDF) is a function [Formula: see text] having the property that: (i) every vertex [Formula: see text] with f(v) = 0 has a neighbor u with f(u) = 3 or at least two ...
F. Nahani Pour +3 more
doaj +2 more sources
On the Independent Double Roman Domination in Graphs [PDF]
Bulletin of the Iranian Mathematical Society, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Doost Ali Mojdeh, Zhila Mansouri
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Computational Complexity of Outer-Independent Total and Total Roman Domination Numbers in Trees
IEEE Access, 2018 An outer-independent total dominating set (OITDS) of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent.
Zepeng Li +4 more
doaj +3 more sources
(Independent) Roman Domination Parameterized by Distance to Cluster
International Conference on Combinatorial Optimization and ApplicationsarXiv admin note: text overlap with arXiv:2405.10556 by other ...
Ashok, Pradeesha +4 more
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Lower bounds on the Roman and independent Roman domination numbers
Applicable Analysis and Discrete Mathematics, 2016 A Roman dominating function (RDF) on a graph G is a function f : V (G) ? {0,1,2} satisfying the condition that every vertex u with f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2. The weight of a Roman dominating function is the sum f(V) = ?v?V f(v), and the minimum weight of a Roman dominating function f is the Roman ...
Chellali, Mustapha +2 more
openaire +4 more sources