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Signed Total Roman Domination in Digraphs

Discussiones Mathematicae Graph Theory, 2017
Let D be a finite and simple digraph with vertex set V (D). A signed total Roman dominating function (STRDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) ∑x∈N−(v)f(x) ≥ 1 for each v ∈ V (D), where N−(v) consists ...
Volkmann Lutz
doaj   +1 more source

Bounds on the restrained Roman domination number of a graph

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, S.R‎. ‎Mirmehdipour   +1 more
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Varieties of Roman domination IV

AKCE International Journal of Graphs and Combinatorics
Roman domination was introduced in 2004 by Cockayne, Dreyer, Hedetniemi, and Hedetniemi. If [Formula: see text] is the vertex set of a graph G, then a function [Formula: see text] is a Roman dominating function if every vertex [Formula: see text] for ...
M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, L. Volkmann   +3 more
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Computational Complexity of Outer-Independent Total and Total Roman Domination Numbers in Trees

IEEE Access, 2018
An outer-independent total dominating set (OITDS) of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent.
Zepeng Li, Zehui Shao, Fangnian Lang, Xiaosong Zhang, Jia-Bao Liu   +4 more
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Perfect Roman and Perfect Italian Domination of Cartesian Product Graphs

Scientific Journal of King Faisal University: Basic and Applied Sciences
For a graph G=(V,E), a function f:V→{0,1,2} is a perfect Roman dominating function (PRDF) on G if every v∈V with f(v)=0 is adjacent to exactly one vertex u with f(u)=2. The sum ∑_(v∈V)^▒f (v) is the weight w(f) of f.
Ahlam Almulhim
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An Upper Bound for the Eternal Roman Domination Number

Mathematics
Imagine using mobile guards to defend the vertices of a graph G from a sequence of attacks subject to the conditions that after each attack: (i) each guard either remains in place or moves to an adjacent vertex; (ii) the configuration of guards forms a ...
Richard Brewster, Gary MacGillivray, Ethan Williams   +2 more
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Perfect Roman {3}-Domination in Graphs: Complexity and Bound of Perfect Roman {3}-Domination Number of Trees

Journal of Mathematics
A perfect Roman 3-dominating function on a graph G=V,E is a function f:V⟶0,1,2,3 having the property that if fv=0, then ∑u∈Nvfu=3, and if fv=1, then ∑u∈Nvfu=2 for any vertex v∈V.
Ahlam Almulhim
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Further results on outer independent triple Roman domination

AKCE International Journal of Graphs and Combinatorics
An outer-independent triple Roman dominating function (OI[3]RDF) on a graph [Formula: see text] is function [Formula: see text] having the property that (i) if [Formula: see text] then v must have either a neighbor assigned 4 or two neighbors one of ...
F. Najafi, J. Amjadi, S. M. Sheikholeslami, M. Chellali, S. Kosari   +4 more
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Domination parameters of generalized Sierpiński graphs

AKCE International Journal of Graphs and Combinatorics
In this paper, we obtain the Italian domination number, perfect Italian domination number and double Roman domination number of generalized Sierpiński graph [Formula: see text] where G is a cycle Cn, [Formula: see text] a complete bipartite graph ...
Jismy Varghese, V. Anu, Lakshmanan S. Aparna   +2 more
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Co-Roman dominating of girds

پژوهش‌های ریاضی, 2022
Rana Khoeilr, marzieh soroudi, Maryam Atapour   +2 more
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