Results 11 to 20 of about 72,600 (248)
On the Total Double Roman Domination
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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Double Roman reinforcement number in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 For a graph a double Roman dominating function is a function having the property that if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(v) = 1, then vertex v must have at least one ...
J. Amjadi, H. Sadeghi
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Bounds on the Double Italian Domination Number of a Graph
Discussiones Mathematicae Graph Theory, 2022 For a graph G, a Roman {3}-dominating function is a function f : V → {0, 1, 2, 3} having the property that for every vertex u ∈ V, if f(u) ∈ {0, 1}, then f(N[u]) ≥ 3.
Azvin Farzaneh, Rad Nader Jafari
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Bounds on signed total double Roman domination [PDF]
Communications in Combinatorics and Optimization, 2020 A signed total double Roman dominating function (STDRDF) on {an} isolated-free graph $G=(V,E)$ is a function $f:V(G)\rightarrow\{-1,1,2,3\}$ such that (i) every vertex $v$ with $f(v)=-1$ has at least two neighbors assigned 2 under $f$ or one neighbor ...
L. Shahbazi +3 more
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Further results on independent double roman trees
AKCE International Journal of Graphs and Combinatorics, 2022 A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v
A. Rahmouni +3 more
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Bounds on the total double Roman domination number of graphs
Discussiones Mathematicae Graph Theory, 2023 Summary: Let \(G\) be a simple graph with no isolated vertex and let \(\gamma_{tdR}(G)\) be the total double Roman domination number of \(G\). In this paper, we present lower and upper bounds on \(\gamma_{tdR}(G)\) of a graph \(G\) in terms of the order, open packing number and the numbers of support vertices and leaves, and we characterize all ...
Hao, Guoliang +3 more
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On the Outer-Independent Double Roman Domination of Graphs
Frontiers in Applied Mathematics and Statistics, 2021 An outer-independent double Roman dominating function (OIDRDF) of a graph G is a function h:V(G)→{0,1,2,3} such that i) every vertex v with f(v)=0 is adjacent to at least one vertex with label 3 or to at least two vertices with label 2, ii) every vertex ...
Yongsheng Rao +4 more
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, 2007 This is a preprint (author's original) version of an article published in The American Journal of Philology in 2007. The final version of this article may be found at http://muse.jhu.edu/journals/ajp/ (login may be required).
Uden, James
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Domination parameters with number 2: Interrelations and algorithmic consequences [PDF]
, 2018 In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination ...
Bonomo, Flavia +4 more
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Double Roman Graphs in P(3k, k)
Mathematics, 2021 A double Roman dominating function on a graph G=(V,E) is a function f:V→{0,1,2,3} with the properties that if f(u)=0, then vertex u is adjacent to at least one vertex assigned 3 or at least two vertices assigned 2, and if f(u)=1, then vertex u is ...
Zehui Shao +5 more
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