Results 51 to 60 of about 5,939,930 (166)
Effect of vertex deletion on the weak Roman domination number of a graph
AKCE International Journal of Graphs and Combinatorics, 2019 Let be a graph and be a function. The weight of a vertex is and a vertex with weight is said to be undefended with respect to , if it is not adjacent to a vertex with positive weight. The function is a weak Roman dominating function (WRDF) if each vertex
P. Roushini Leely Pushpam, M. Kamalam
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THE ROMAN BONDAGE NUMBER OF A DIGRAPH
, 2016 Let D=(V,A)D=(V,A) be a finite and simple digraph. A Roman dominating function on DD is a labeling f:V(D)→{0,1,2}f:V(D)→{0,1,2} such that every vertex with label 0 has an in-neighbor with label 2.
Sheikholeslami, Seyed Mahmoud;Dehgardi, Nasrin;Volkmann, Lutz;Meierling, Dirk +4 more
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The Perfect Roman Domination Number of the Cartesian Product of Some Graphs
Journal of Mathematics, 2022 A perfect Roman dominating function on a graph G is a function f:VG⟶0,1,2 for which every vertex v with fv=0 is adjacent to exactly one neighbor u with fu=2. The weight of f is the sum of the weights of the vertices.
Ahlam Almulhim +2 more
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Bounds on the locating Roman dominating number in trees [PDF]
, 2018 A Roman dominating function (or just RDF) on a graph $ G = (V, E) $ is a function $ f : V \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 $f(v) = 2$.
Rahbani, Hadi +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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Long Dominating Cycles in Graphs [PDF]
, 2007 All graphs considered in this paper will be finite and simple.
Zhiren, Sun, Yongga, A.
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The Signed Total Roman k-Domatic Number Of A Graph
Discussiones Mathematicae Graph Theory, 2017 Let k ≥ 1 be an integer. A signed total Roman k-dominating function on a graph G is a function f : V (G) → {−1, 1, 2} such that Ʃu2N(v) f(u) ≥ k for every v ∈ V (G), where N(v) is the neighborhood of v, and every vertex u ∈ V (G) for which f(u) = −1 is ...
Volkmann Lutz
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Total Roman domination for proper interval graphs
Electronic Journal of Graph Theory and Applications, 2020 A function f:V → {0,1,2} is a total Roman dominating function (TRDF) on a graph G=(V,E) if for every vertex v ∈ V with f(v) = 0 there is a vertex u adjacent to v with f(u) = 2 and for every vertex v ∈ V with f(v) > 0 there exists a vertex u ∈ NG(v ...
Abolfazl Poureidi
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Extremal Graphs for a Bound on the Roman Domination Number
Discussiones Mathematicae Graph Theory, 2020 A Roman dominating function on a graph G = (V, E) is a function f:V (G) → {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman dominating function is the value w(f) = Σu∈V(G)f(u).
Bouchou Ahmed +2 more
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The signed Roman domatic number of a digraph
Electronic Journal of Graph Theory and Applications, 2015 Let $D$ be a finite and simple digraph with vertex set $V(D)$.A {\em signed Roman dominating function} on the digraph $D$ isa function $f:V (D)\longrightarrow \{-1, 1, 2\}$ such that$\sum_{u\in N^-[v]}f(u)\ge 1$ for every $v\in V(D)$, where $N^-[v ...
Seyed Mahmoud Sheikholeslami +1 more
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