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Vertex-edge perfect Roman domination number
AIMS Mathematics, 2023 A vertex-edge perfect Roman dominating function on a graph $ G = (V, E) $ (denoted by ve-PRDF) is a function $ f:V\left(G\right)\longrightarrow\{0, 1, 2\} $ such that for every edge $ uv\in E $, $ \max\{f(u), f(v)\}\neq0 $, or $ u $ is adjacent to ...
Bana Al Subaiei +2 more
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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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Maximum Second Zagreb Index Of Trees With Given Roman Domination Number [PDF]
Transactions on Combinatorics, 2023 Chemical study regarding total $\pi$-electron energy with respect to conjugated molecules has focused on the second Zagreb index of graphs. Moreover, in the last half-century, it has gotten a lot of attention.
Ayu Ameliatul Ahmad Jamri +3 more
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AIMS Mathematics, 2023 Let $ G = (V, E) $ be a simple graph with vertex set $ V $ and edge set $ E $, and let $ f $ be a function $ f:V\mapsto \{0, 1, 2\} $. A vertex $ u $ with $ f(u) = 0 $ is said to be undefended with respect to $ f $ if it is not adjacent to a vertex with ...
Jian Yang, Yuefen Chen, Zhiqiang Li
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Discussiones Mathematicae Graph Theory, 2022 A 2-rainbow dominating function (2RDF) of a graph G is a function g from the vertex set V (G) to the family of all subsets of {1, 2} such that for each vertex v with g(v) =∅ we have ∪u∈N(v) g(u) = {1, 2}.
Poureidi Abolfazl, Rad Nader Jafari
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Triple Roman domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2022 For a graph $G=(V, E)$, a triple Roman domination function is a function $f: V(G)\longrightarrow\{0, 1, 2, 3, 4\}$ having the property that for any vertex $v\in V(G)$, if $f(v)
Jafar Amjadi, Hakimeh Sadeghi
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Total Roman Domination Number of Rooted Product Graphs [PDF]
Mathematics, 2020 Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. If f satisfies that every vertex in the set {v∈V(G):f(v)=0} is adjacent to at least one vertex in the set {v∈V(G):f(v)=2}, and if the subgraph induced by the set {v∈V(G):f(v)≥1} has ...
Abel Cabrera Martínez +3 more
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On the Strong Roman Domination Number of Graphs [PDF]
Discrete Applied Mathematics, 2015 Based on the history that the Emperor Constantine decreed that any undefended place (with no legions) of the Roman Empire must be protected by a "stronger" neighbor place (having two legions), a graph theoretical model called Roman domination in graphs was described. A Roman dominating function for a graph $G=(V,E)$, is a function $f:V\rightarrow \{0,1,
M. P. Álvarez-Ruiz +4 more
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On [k]-Roman domination subdivision number of graphs
AKCE International Journal of Graphs and Combinatorics, 2022 Let [Formula: see text] be an integer and G a simple graph with vertex set V(G). Let f be a function that assigns labels from the set [Formula: see text] to the vertices of G.
K. Haghparast +3 more
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Extremal Graphs for a Bound on the Roman Domination Number
Discussiones Mathematicae Graph Theory, 2020 A Roman dominating function on a graph G = (V, E) is a function f:V (G) → {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman dominating function is the value w(f) = Σu∈V(G)f(u).
Bouchou Ahmed +2 more
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