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INVERSE ROMAN DOMINATION IN GRAPHS

Discrete Mathematics, Algorithms and Applications, 2013
Motivated by the article in Scientific American [7], Michael A Henning and Stephen T Hedetniemi explored the strategy of defending the Roman Empire. Cockayne defined Roman dominating function (RDF) on a Graph G = (V, E) to be a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex
M. Kamal Kumar, L. Sudershan Reddy
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Cost-Effective Network Optimization using Middle Weak Roman Domination with Python Integration

2025 4th International Conference on Distributed Computing and Electrical Circuits and Electronics (ICDCECE)
Middle weak Roman domination is an important graph theory concept that has important applications in defense, network design, optimization, and resource management.
st J. Meena, N. Malini
semanticscholar   +1 more source

Isolate Roman domination in graphs

Discrete Mathematics, Algorithms and Applications, 2021
Let [Formula: see text] be a graph with the vertex set [Formula: see text]. A function [Formula: see text] is called a Roman dominating function of [Formula: see text], if every vertex [Formula: see text] with [Formula: see text] is adjacent to at least one vertex [Formula: see text] with [Formula: see text].
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Triple Roman Domination Number of Circulant Graph

2025 7th International Conference on Information Science, Electrical and Automation Engineering (ISEAE)
Roman domination is a famous topic in graph theory originated from a defense strategy of Ancient Rome. Roman legions are deployed in some important military areas so that any attack could be resisted by a local legion or a supported legion from an ...
Yuting Wang, Shuyan Du, Siyu Wang, Hong Gao   +3 more
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Roman [1,2]-domination of graphs

Applied Mathematics and Computation
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guoliang Hao, Xiaodan Chen, Seyed Mahmoud Sheikholeslami, Haining Jiang   +3 more
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Signed Roman domination in digraphs

Journal of Combinatorial Optimization, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seyed Mahmoud Sheikholeslami, Lutz Volkmann   +1 more
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Double Roman domination number

Discrete Applied Mathematics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anu V., S. Aparna Lakshmanan
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Exploring Algorithmic Solutions for the Independent Roman Domination Problem in Graphs

Discrete Applied Mathematics
Given a graph $G=(V,E)$, a function $f:V\to \{0,1,2\}$ is said to be a \emph{Roman Dominating function} if for every $v\in V$ with $f(v)=0$, there exists a vertex $u\in N(v)$ such that $f(u)=2$.
Kaustav Paul, Ankit Sharma, Arti Pandey
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Double Roman Domination in Cartesian Product

Creative Mathematics and Informatics
Given a graph $G=(V,E)$, a function $f:V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then there exist $ v_{1},v_{2}\in N(v)$ such that $f(v_{1})=2=f(v_{2})$ or there exists $ w \in N(v)$ such that $f(w)=3$, and if $f(v)=1$, then there ...
V. Anu, L. Aparna
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Algorithmic Results for Weak Roman Domination Problem in Graphs

Discrete Applied Mathematics
Consider a graph $G = (V, E)$ and a function $f: V \rightarrow \{0, 1, 2\}$. A vertex $u$ with $f(u)=0$ is defined as \emph{undefended} by $f$ if it lacks adjacency to any vertex with a positive $f$-value.
Kaustav Paul, Ankit Sharma, Arti Pandey
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