Results 41 to 50 of about 1,370 (272)
Roman domination in oriented trees
Electronic Journal of Graph Theory and Applications, 2021 Let D=(V,A) be a digraph of order n = |V|. A Roman dominating function of a digraph D is a function f : V → {0,1,2} such that every vertex u for which f(u) = 0 has an in-neighbor v for which f(v) = 2.
Lyes Ouldrabah +2 more
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Counting the Number of Minimum Roman Dominating Functions of a Graph
CoRR, 2014 We provide two algorithms counting the number of minimum Roman dominating functions of a graph on n vertices in O(1.5673^n) time and polynomial space. We also show that the time complexity can be reduced to O(1.5014^n) if exponential space is used. Our result is obtained by transforming the Roman domination problem into other combinatorial problems on ...
Zheng Shi, Khee Meng Koh
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On interior Roman domination in graphs
Indonesian Journal of CombinatoricsLet G = (V(G), E(G)) be a non-complete graph and let ϕ:V(G)→{0,1,2} be a function on G. For each i ∈ {0, 1, 2}, let Vi={w ∈ V(G): ϕ(w)=i}. A function ϕ=(V0, V1, V2) is an interior Roman dominating function (InRDF) on G if (i) for every v ∈ V0, there ...
Leomarich F. Casinillo
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A note on the double Roman domination number of graphs [PDF]
, 2020 summary:For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least two neighbors assigned $2$ under $f$ or one neighbor with $f(w)
Chen, Xue-Gang
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A Borane Sandwich Analogue of Ferrocene
Angewandte Chemie, EarlyView.The first ferrocene analogue with two boron‐based ligands is identified through a global exploration of the FeB10H20 potential energy surface. The η5,η5‐Fe(B5H10)2 complex emerges as the global minimum, showing that metal coordination inverts borane stability and enables aromatic boron rings inaccessible in isolation.
Viviana Roman‐Ventura +8 more
wiley +2 more sources
The Distance Roman Domination Numbers of Graphs
Discussiones Mathematicae Graph Theory, 2013 Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k ...
Aram Hamideh +2 more
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On the complexity of some hop domination parameters
Electronic Journal of Graph Theory and Applications, 2019 A hop Roman dominating function (HRDF) on a graph G = (V, E) is a function f : V → {0, 1, 2} having the property that for every vertex v ∈ V with f(v) = 0 there is a vertex u with f(u) = 2 and d(u, v) = 2. The weight of an HRDF f is the sum of its values
Nader Jafari Rad, Elahe Shabani
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The Double Roman Domatic Number of a Digraph
Discussiones Mathematicae Graph Theory, 2020 A double Roman dominating function on a digraph D with vertex set V (D) is defined in [G. Hao, X. Chen and L. Volkmann, Double Roman domination in digraphs, Bull. Malays. Math. Sci. Soc. (2017).] as a function f : V (D) → {0, 1, 2, 3} having the property
Volkmann Lutz
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Total double Roman domination in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:V\rightarrow\{0,1,2,3\}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one ...
Guoliang Hao +2 more
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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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