Results 21 to 30 of about 571 (202)
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
doaj +1 more source
On The Total Roman Domination in Trees
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by ...
Amjadi Jafar +2 more
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
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
doaj +1 more source
Angewandte Chemie, EarlyView.Homochiral Cu(I) cyanide complexes based on 2,2’‐bis(diphenylphosphino)‐1,1’‐binaphthyl (BINAP) form melt‐quenched and desolvation‐derived metal–organic glasses that exhibit circularly polarized thermally activated delayed fluorescence (TADF) at room temperature, enabling processable chiroptical materials.
Zeyu Fan +5 more
wiley +2 more sources
Dominating the Direct Product of Two Graphs through Total Roman Strategies
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
doaj +1 more source
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
doaj +1 more source