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Total Roman {2}-Dominating Functions in Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2022 A Roman {2}-dominating function (R2F) is a function f : V → {0, 1, 2} with the property that for every vertex v ∈ V with f(v) = 0 there is a neighbor u of v with f(u) = 2, or there are two neighbors x, y of v with f(x) = f(y) = 1.
Ahangar H. Abdollahzadeh +3 more
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Restrained condition on double Roman dominating functions [PDF]
Applied Mathematics and Computation, 2023 We continue the study of restrained double Roman domination in graphs. For a graph $G=\big{(}V(G),E(G)\big{)}$, a double Roman dominating function $f$ is called a restrained double Roman dominating function (RDRD function) if the subgraph induced by $\{v\in V(G)\mid f(v)=0\}$ has no isolated vertices. The restrained double Roman domination number (RDRD
Mustapha Chellali +2 more
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Strong Equality of Perfect Roman and Weak Roman Domination in Trees [PDF]
Mathematics, 2019 Let G = ( V , E ) be a graph and f : V ⟶ { 0 , 1 , 2 } be a function. Given a vertex u with f ( u ) = 0 , if all neighbors of u have zero weights, then u is called undefended with respect to f. Furthermore, if every vertex u with
Abdollah Alhevaz +3 more
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Signed total double Roman dominating functions in graphs [PDF]
AKCE International Journal of Graphs and CombinatoricsA signed total double Roman dominating function (STDRDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex v with [Formula: see text] has at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, (ii) every vertex v with f(v) = 1 has at least one neighbor w with [Formula: see ...
Seyed Mahmoud Sheikholeslami +1 more
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Unique response strong Roman dominating functions of graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2021 Given a simple graph G=(V,E) with maximum degree Δ. Let (V0, V1, V2) be an ordered partition of V, where Vi = {v ∈ V : f(v)=i} for i = 0, 1 and V2 = {v ∈ V : f(v)≥2}.
Doost Ali Mojdeh +3 more
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Roman Census: Enumerating and Counting Roman Dominating Functions on Graph Classes [PDF]
, 2023 The concept of Roman domination has recently been studied concerning enumerating and counting (WG 2022). It has been shown that minimal Roman dominating functions can be enumerated with polynomial delay, contrasting what is known about minimal dominating sets.
Faisal N. Abu-Khzam +2 more
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On the total and strong version for Roman dominating functions in graphs [PDF]
Aequationes Mathematicae, 2021 19 ...
Ismael G Yero +2 more
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Bounds on the restrained Roman domination number of a graph [PDF]
Communications in Combinatorics and Optimization, 2016 A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) =2$.
H. Abdollahzadeh Ahangar +1 more
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A note on k-Roman graphs [PDF]
Opuscula Mathematica, 2013 Let \(G=\left(V,E\right)\) be a graph and let \(k\) be a positive integer. A subset \(D\) of \(V\left( G\right) \) is a \(k\)-dominating set of \(G\) if every vertex in \(V\left( G\right) \backslash D\) has at least \(k\) neighbours in \(D\).
Ahmed Bouchou +2 more
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Some Properties of Double Roman Domination [PDF]
Discrete Dynamics in Nature and Society, 2020 A double Roman dominating function on a graph G is a function f:VG⟶0,1,2,3 satisfying the conditions that every vertex u for which fu=0 is adjacent to at least one vertex v for which fv=3 or two vertices v1 and v2 for which fv1=fv2=2 and every vertex u ...
Hong Yang, Xiaoqing Zhou
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