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On the Total Double Roman Domination [PDF]
IEEE Access, 2019 Let G = (V, E) be a simple graph. A double Roman dominating function (DRDF) on G is a function f from the vertex set V of G into {0, 1, 2, 3} such that if f (u) = 0, then u must have at least two neighbors assigned 2 or one neighbor assigned 3 under f ...
Zehui Shao +3 more
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Quaestiones Mathematicae, 2015 A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination numberγt(G). A Roman dominating function on a graph G is a function
Haynes, Teresa W. +2 more
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Dominating the Direct Product of Two Graphs through Total Roman Strategies [PDF]
Mathematics, 2020 Given a graph G without isolated vertices, a total Roman dominating function for G is a function f:V(G)→{0,1,2} such that every vertex u with f(u)=0 is adjacent to a vertex v with f(v)=2, and the set of vertices with positive labels induces a graph of ...
Abel Cabrera Martínez +3 more
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Total Weak Roman Domination in Graphs [PDF]
Symmetry, 2019 Given a graph G = ( V , E ) , a function f : V → { 0 , 1 , 2 , ⋯ } is said to be a total dominating function if ∑ u ∈ N ( v ) f ( u ) > 0 for every v ∈ V , where N ( v ) denotes the open ...
Juan A. Rodríguez-Velázquez +2 more
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Global total Roman domination in graphs
Discrete Mathematics, Algorithms and Applications, 2017 A total Roman dominating function (TRDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the conditions (i) every vertex [Formula: see text] for which [Formula: see text] is adjacent at least one vertex [Formula: see text ...
J. Amjadi +2 more
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Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees
Mathematics, 2021 For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v ...
Xinyue Liu +3 more
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Quasi total double Roman domination in graphs
AKCE International Journal of Graphs and CombinatoricsA quasi total double Roman dominating function (QTDRD-function) on a graph [Formula: see text] is a function [Formula: see text] having the property that (i) if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w
S. Kosari +4 more
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Signed total Roman $k$-domination in directed graphs
Communications in Combinatorics and Optimization, 2016 Let $D$ be a finite and simple digraph with vertex set $V(D)$. A signed total Roman $k$-dominating function (STR$k$DF) on $D$ is a function $f:V(D)\rightarrow\{-1, 1, 2\}$ satisfying the conditions that (i) $\sum_{x\in N^{-}(v)}f(x)\ge k ...
N. Dehgard, L. Volkmann
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Quasi-total Roman reinforcement in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 A quasi-total Roman dominating function (QTRD-function) on [Formula: see text] is a function [Formula: see text] such that (i) every vertex x for which f(x) = 0 is adjacent to at least one vertex v for which f(v) = 2, and (ii) if x is an isolated vertex ...
N. Ebrahimi +3 more
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Outer-independent total Roman domination in graphs [PDF]
Discrete Applied Mathematics, 2019 Given a graph $G$ with vertex set $V$, a function $f:V\rightarrow \{0,1,2\}$ is an outer-independent total Roman dominating function on $G$ if \begin{itemize} \item every vertex $v\in V$ for which $f(v)=0$ is adjacent to at least one vertex $u\in V ...
González Yero, Ismael +5 more
core +3 more sources