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Graphs with Large Hop Roman Domination Number [PDF]
Computer Science Journal of Moldova, 2019 A subset $S$ of vertices of a graph $G$ is a hop dominating set if every vertex outside $S$ is at distance two from a vertex of $S$. A Roman dominating function on a graph $G=(V,E)$ is a function $f: V(G) \longrightarrow \{0, 1, 2\}$ satisfying the ...
E. Shabani, N. Jafari Rad, A. Poureidi
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[k]-Roman Domination in Digraphs
Symmetry, 2023 Let D=(V(D),A(D)) be a finite, simple digraph and k a positive integer. A function f:V(D)→{0,1,2,…,k+1} is called a [k]-Roman dominating function (for short, [k]-RDF) if f(AN−[v])≥|AN−(v)|+k for any vertex v∈V(D), where AN−(v)={u∈N−(v):f(u)≥1} and AN−[v]=AN−(v)∪{v}. The weight of a [k]-RDF f is ω(f)=∑v∈V(D)f(v).
Xinhong Zhang, Xin Song, Ruijuan Li
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ALGORITHMIC ASPECTS OF ROMAN GRAPHS [PDF]
Journal of Algebraic Systems, 2021 Let $G=(V, E)$ be a graph. A set $S \subseteq V$ is called a dominating set of $G$ if for every $v\in V-S$ there is at least one vertex $u \in N(v)$ such that $u\in S$.
A. Poureidi
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Complexity and Exact Values for [k]-Roman and Strong Roman Domination for Specific Graph Families
MathematicsMotivated by the original idea of defending the Roman Empire, all these domination concepts can be interpreted as vertex-labeling schemes that model the allocation of resources to protect a graph against attacks.
Juan Carlos Valenzuela-Tripodoro +3 more
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Bounds on the Double Italian Domination Number of a Graph
Discussiones Mathematicae Graph Theory, 2022 For a graph G, a Roman {3}-dominating function is a function f : V → {0, 1, 2, 3} having the property that for every vertex u ∈ V, if f(u) ∈ {0, 1}, then f(N[u]) ≥ 3.
Azvin Farzaneh, Rad Nader Jafari
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Annals of Mathematics and Computer ScienceA graph associated to a finite group is a way to analyze some properties of a group graphically. Many graphs of groups have been constructed according to the properties of the groups such as the commuting and non-commuting graphs.
Akram Alqesmah, Deepak Gangabylaiah
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On the co-Roman domination in graphs
Discussiones Mathematicae Graph Theory, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zehui Shao +4 more
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A note on the independent roman domination in unicyclic graphs [PDF]
Opuscula Mathematica, 2012 A Roman dominating function (RDF) on a graph \(G = (V;E)\) is a function \(f : V \to \{0, 1, 2\}\) satisfying the condition that every vertex \(u\) for which \(f(u) = 0\) is adjacent to at least one vertex \(v\) for which \(f(v) = 2\).
Mustapha Chellali, Nader Jafari Rad
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Super Hop Roman Domination in Graphs
European Journal of Pure and Applied MathematicsLet $G = (V(G), E(G))$ be a simple undirected graph. A function $f:V(G)\rightarrow \{0,1,2\}$ is a super hop Roman dominating function (SHRDF) on $G$ if for every $v\in V(G)$ with $f(v)=0$, there exist $w, u \in V(G)$ with $f(w) = 2$ and $f(u) \ne 0 ...
Leomarich F. Casinillo +1 more
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On the Total Version of Triple Roman Domination in Graphs
MathematicsIn this paper, we describe the study of total triple Roman domination. Total triple Roman domination is an assignment of labels from {0,1,2,3,4} to the vertices of a graph such that every vertex is protected by at least three units either on itself or ...
Juan Carlos Valenzuela-Tripodoro +3 more
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