Results 41 to 50 of about 129,618 (274)

ALGORITHMIC ASPECTS OF ROMAN GRAPHS [PDF]

Journal of Algebraic Systems, 2021
Let $G=(V, E)$ be a graph. A set $S \subseteq V$ is called a dominating set of $G$ if for every $v\in V-S$ there is at least one vertex $u \in N(v)$ such that $u\in S$.
A. Poureidi
doaj   +1 more source

Complexity and Exact Values for [k]-Roman and Strong Roman Domination for Specific Graph Families

Mathematics
Motivated by the original idea of defending the Roman Empire, all these domination concepts can be interpreted as vertex-labeling schemes that model the allocation of resources to protect a graph against attacks.
Juan Carlos Valenzuela-Tripodoro, María Antonia Mateos-Camacho, Martín Cera López, María Pilar Álvarez-Ruíz   +3 more
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, Luis Quispe‐Corimayhua, Dumer S. Sacanamboy, Diego Inostroza, Luis Leyva‐Parra, Dayán Páez, Kelling J. Donald, Gabriel Merino, William Tiznado   +8 more
wiley   +2 more sources

A note on the independent roman domination in unicyclic graphs [PDF]

Opuscula Mathematica, 2012
A Roman dominating function (RDF) on a graph \(G = (V;E)\) is a function \(f : V \to \{0, 1, 2\}\) satisfying the condition that every vertex \(u\) for which \(f(u) = 0\) is adjacent to at least one vertex \(v\) for which \(f(v) = 2\).
Mustapha Chellali, Nader Jafari Rad
doaj   +1 more source

Rainbow domination and related problems on some classes of perfect graphs [PDF]

, 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, A Bretscher, B Bres̆ar, B Bres̆ar, B Courcelle, B Hartnell, B Jamison, C Yen, D Corneil, D Corneil, F Chu, G Chang, G Chang, J Rooij van, M Farber, M Golumbic, M Habib, P Cameron, P Gilmore, R Aharoni, R Rubalcaba, R Rubalcaba, T Gallai, V Vizing   +23 more
core   +2 more sources

Circularly Polarized Luminescent and Melt‐Processable Copper(I)‐Organic Glasses Based on 2,2′‐Bis(diphenylphosphino)‐1,1′‐binaphthyl

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, Indranil Sen, Roman Pallach, Guo‐Qiang Li, Andreas Steffen, Sebastian Henke   +5 more
wiley   +2 more sources

On the Total Version of Triple Roman Domination in Graphs

Mathematics
In this paper, we describe the study of total triple Roman domination. Total triple Roman domination is an assignment of labels from {0,1,2,3,4} to the vertices of a graph such that every vertex is protected by at least three units either on itself or ...
Juan Carlos Valenzuela-Tripodoro, Maria Antonia Mateos-Camacho, Martin Cera, Maria Pilar Alvarez-Ruiz   +3 more
doaj   +1 more source

Survey on Roman {2}-Domination

Mathematics
The notion of Roman {2}-domination was introduced in 2016 as a variant of Roman domination, a concept inspired by a defending strategy used by the emperor Constantine (272–337 AD) to protect the Roman Empire.
Ahlam Almulhim, Bana Al Subaiei, Saiful Rahman Mondal   +2 more
doaj   +1 more source

Super‐Resolution Ultrasound Based Cell Tracking With Polymeric Nanobubbles

Advanced Materials, EarlyView.
This study presents a super‐resolution ultrasound platform for tracking cells in vivo. Biocompatible polymeric nanobubbles are used as highly echogenic intracellular labels. Following the injection of cells and microbubbles, ultrasound localization microscopy (ULM) can dynamically match the microvascular architecture and individual cell trajectories ...
Junlin Chen, Xiaoyu Wang, Jilin Fan, Bi Wang, Hanghang Fang, Yurui Wang, Hao Cui, Mohammad Roufarshbaf, Ekaterina Savina, Alexandra Valeske, Quim Peña, Yang Shi, Andreas Herrmann, Twan Lammers, Mathias Hornef, Roman Barmin, Thomas Lisson, Georg Schmitz, Anne Rix, Fabian Kiessling   +19 more
wiley   +1 more source

Triple Roman domination subdivision number in graphs [PDF]

Computer Science Journal of Moldova, 2022
For a graph $G=(V, E)$, a triple Roman domination function is a function $f: V(G)\longrightarrow\{0, 1, 2, 3, 4\}$ having the property that for any vertex $v\in V(G)$, if $f(v)
Jafar Amjadi, Hakimeh Sadeghi
doaj