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On the Total and Strong Version for Roman Dominating Functions in Graphs [PDF]

Aequationes Mathematicae, 2021
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Ismael Gonzalez Yero, Seyed Mahmoud Sheikholeslami   +1 more
exaly   +4 more sources

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Outer Independent Roman Dominating Functions in Graphs

International Journal of Computer Mathematics, 2017
ABSTRACTA Roman dominating function (RDF) on a graph G is a function f:V(G)→{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 function f:V(G)→{0,1,2} is an outer-independent Roman dominating function (OIRDF) on G if f is an RDF and V0 is an independent set.
Mustapha Chellali, Vladimir Samodivkin, Hossein Abdollahzadeh Ahangar   +2 more
exaly   +3 more sources

Total Modern Roman Dominating Functions in Graphs

European Journal of Pure and Applied Mathematics
Let $G=(V(G), E(G))$ be any connected graph. A function $f:V(G)\to \{0,1,2,3\}$ is a modern Roman dominating  function of $G$ if for each $v\in V(G)$ with $f(v)=0$, there exist $u,w \in N_G (v)$ such that $f(u)=2$ and $f(w)=3$; andfor each $v\in V(G)$ with $f(v)=1$, there exists $u \in N_G (v)$ such that $f(u)=2$ or $f(u)=3$.
Ferdinand Jamil
exaly   +2 more sources

Trees With Unique Roman Dominating Functions of Minimum Weight

Discrete Mathematics, Algorithms and Applications, 2014
A Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2} satisfying the condition that every vertex u of G for which 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 value f(V(G)) = ∑u∈V(G)f(u).
Nader Jafari Rad
exaly   +3 more sources

Modern Roman Dominating Functions in Graphs

European Journal of Pure and Applied Mathematics
Let $G=(V(G), E(G))$ be any connected graph. A function $f:V(G) \to \{0,1,2,3\}$ is a modern Roman dominating function of $G$ if for each $v\in V(G)$ with $f(v)=0$, there exist $u,w \in N_G (v)$ such that $f(u)=2$ and $f(w)=3$; and for each $v\in V(G)$ with $f(v)=1$, there exists $u \in N_G (v)$ such that $f(u)=2$ or $f(w)=3$.
Sherihatha Ahamad, Jerry Boy G. Cariaga, Sheila M. Menchavez   +2 more
exaly   +2 more sources

Fair Hop Roman Dominating Function in Graphs

Annals of Mathematics and Computer Science
This paper introduces a new variant of a hop Roman dominating function in graphs called the fair hop Roman dominating function. Moreover, several important combinatorial properties and characterizations of fair hop Roman dominating functions in various graph classes were investigated.
exaly   +2 more sources

Algorithmic complexity of triple Roman dominating functions on graphs

2023
Summary: Given a graph \(G=(V,E)\), a function \(f:V\to \{0,1,2,3,4\}\) is a triple Roman dominating function (TRDF) of \(G\), for each vertex \(v\in V\), (i) if \(f (v) = 0 \), then \(v\) must have either one neighbour in \(V_4\), or either two neighbours in \(V_2 \cup V_3\) (one neighbour in \(V_3)\) or either three neighbours in \(V_2\), (ii) if \(f
Poureidi, Abolfazl, Fathali, Jafar
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Connected Roman Hop Dominating Functions in Graphs

European Journal of Pure and Applied Mathematics
Let $G$ be a connected graph. A hop Roman dominating function $f:V(G)\to \{0,1,2\}$ is a connected hop Roman dominating function (CHRDF) on $G$ if the set $\{u\in V(G): f(u)\neq 0\}$ induces a connected subgraph of $G$. The of weight of a CHRDF f is given by $\omega_G^{cRh}(f)=\sum_{v\in V(G)}f(v)$ and the minimum weight among all connected hop Roman ...
Sérgio Canoy
exaly   +2 more sources

Convex Roman Dominating Functions on Graphs Under Some Binary Operations

European Journal of Pure and Applied Mathematics
Let $G$ be a connected graph. A function $f:V(G)\rightarrow \{0,1,2\}$ is a \textit{convex Roman dominating function} (or CvRDF) if every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$ and $V_1 \cup  V_2$ is convex.
Rona Jane Gamayot Fortosa
exaly   +2 more sources

Outer-Connected Fair Roman Dominating Function in Graphs

Annals of Mathematics and Computer Science
In this paper, we introduce and investigate a new variant of a Roman dominating function in graphs called outer-connected fair Roman dominating function. In addition, we presented some theoretical properties of outer-connected fair Roman dominating functions in some classes of connected graphs and discussed some important results.
Leomarich Casinillo, null Emily Casinillo   +1 more
exaly   +2 more sources