Results 31 to 40 of about 56,401 (136)
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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Nonnegative signed total Roman domination in graphs
Communications in Combinatorics and Optimization, 2020 Let $G$ be a finite and simple graph with vertex set $V(G)$. A nonnegative signed total Roman dominating function (NNSTRDF) on a graph $G$ is a function $f:V(G)\rightarrow\{-1, 1, 2\}$ satisfying the conditions that (i) $\sum_{x\in N(v)}f(x)\ge 0$ for
Nasrin Dehgardi, Lutz Volkmann
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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 +4 more
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On the weak Roman domination number of lexicographic product graphs
, 2018 A vertex $v$ of a graph $G=(V,E)$ is said to be undefended with respect to a function $f: V \longrightarrow \{0,1,2\}$ if $f(v)=0$ and $f(u)=0$ for every vertex $u$ adjacent to $v$.
Pérez-Rosés, Hebert +2 more
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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
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Further Results on the Total Roman Domination in Graphs
Mathematics, 2020 Let G be a graph without isolated vertices. A function f : V ( G ) → { 0 , 1 , 2 } is a total Roman dominating function on G if every vertex v ∈ V ( G ) for which f ( v ) = 0 is adjacent to at least one vertex u ...
Abel Cabrera Martínez +2 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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Total Modern Roman Dominating Functions in Graphs
European Journal of Pure and Applied MathematicsLet $G=(V(G), E(G))$ be any connected graph. A function $f:V(G)\to \{0,1,2,3\}$ is a modern Roman dominating function of $G$ if for each $v\in V(G)$ with $f(v)=0$, there exist $u,w \in N_G (v)$ such that $f(u)=2$ and $f(w)=3$; andfor each $v\in V(G)$ with $f(v)=1$, there exists $u \in N_G (v)$ such that $f(u)=2$ or $f(u)=3$.
Sherihatha Ahamad +3 more
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Zmiany struktury użytkowania ziemi w gospodarstwach rolnych województwa kujawsko-pomorskiego w świetle wyników spisów powszechnych rolnictwa z lat 2002 i 2010 [PDF]
, 2014 The study presents the results of the spatial analysis of the total area of agricultural holdings as of 2010 and the changes in these figures as recorded in 2002 and 2010, whereby the agricultural acreage (including: arable lands, permanent crops and ...
Dubownik, Anna, Rudnicki, Roman
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Rainbow domination and related problems on some classes of perfect graphs
, 2015 Let $k \in \mathbb{N}$ and let $G$ be a graph. A function $f: V(G) \rightarrow 2^{[k]}$ is a rainbow function if, for every vertex $x$ with $f(x)=\emptyset$, $f(N(x)) =[k]$.
A Bertossi +23 more
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