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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
exaly +6 more sources
Fair Secure Roman Dominating Function in Graphs
InPrimeLet G=(V(G),E(G)) be a graph and let ϕ:V(G)→{0,1,2} be a function on G. For each i∈{0,1,2}, let V_i={v∈V(G):ϕ(v)=i}. Then ϕ can be represented as ϕ=(V_0,V_1,V_2).
Leomarich Casinillo, Emily L. Casinillo
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Signed total double Roman dominating functions in graphs
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
exaly +4 more sources
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]
Journal of Computer and System Sciences, 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
openaire +7 more sources
On the total and strong version for Roman dominating functions in graphs [PDF]
Aequationes Mathematicae, 2021 19 ...
Ismael G Yero +1 more
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Strong Equality of Perfect Roman and Weak Roman Domination in Trees
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
doaj +3 more sources
Total Roman domination subdivision number in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 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 $f(v)=2$.
Jafar Amjad
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Minimal Roman Dominating Functions: Extensions and Enumeration
Algorithmica, 2022 AbstractRoman domination is one of the many variants of domination that keeps most of the complexity features of the classical domination problem. We prove that Roman domination behaves differently in two aspects: enumeration and extension. We develop non-trivial enumeration algorithms for minimal Roman dominating functions with polynomial delay and ...
Faisal N. Abu-Khzam +2 more
openaire +2 more sources