Results 41 to 50 of about 86,658 (242)
Total Roman 2-Reinforcement of Graphs
Journal of Mathematics, 2021 A total Roman 2-dominating function (TR2DF) on a graph Γ=V,E is a function l:V⟶0,1,2, satisfying the conditions that (i) for every vertex y∈V with ly=0, either y is adjacent to a vertex labeled 2 under l, or y is adjacent to at least two vertices labeled
M. Kheibari +3 more
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Total roman domination number of graphs
, 2022 In this paper a characterization of minimal total roman dominating functions has been proved. It has also been proved that if v is a pendant vertex and its neighbor u is not a pendant vertex then f(v) = 0 or 1 for any minimal total roman dominating function f. The operation of vertex removal has been considered.
Thakkar, Dineshbhai, Badiyani, Sanket
openaire +1 more source
Coloring, location and domination of corona graphs [PDF]
, 2012 A vertex coloring of a graph $G$ is an assignment of colors to the vertices of $G$ such that every two adjacent vertices of $G$ have different colors. A coloring related property of a graphs is also an assignment of colors or labels to the vertices of a ...
Aguilar, A. Rondón +2 more
core +4 more sources
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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Bimetallic Nanoparticles as Cocatalysts for Photocatalytic Hydrogen Production
Advanced Functional Materials, EarlyView.Recent developments have introduced bimetallic nanoparticles as effective cocatalysts for photocatalytic systems. This review explores the rapidly expanding research on bimetallic cocatalysts for photocatalytic production of hydrogen, emphasizing the creation of carrier‐selective contacts, localized surface plasmon resonance effects, methodologies for ...
Yufen Chen +4 more
wiley +1 more source
On the (total) Roman domination in Latin square graphs
AIMS MathematicsLatin square, also known as Latin square matrix, refers to a kind of $ n\times n $ matrix, in which there are exactly $ n $ different symbols and each symbol appears exactly once in each row and column.
Chang-Xu Zhang +2 more
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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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Emergent Spin‐Glass Behavior in an Iron(II)‐Based Metal–Organic Framework Glass
Advanced Functional Materials, EarlyView.A one‐pot, solvent‐free synthesis yields an Fe2+‐based metal‐organic framework (MOF) glass featuring a continuous random network structure. The material exhibits spin‐glass freezing at 14 K, driven by topological‐disorder and short‐range magnetic frustration, showcasing the potential of MOF glasses as a plattform for cooperative magnetic phenomena in ...
Chinmoy Das +8 more
wiley +1 more source
Acid‐ and Nucleophile‐Gated Photoisomerization of Phosphaindirubin
Angewandte Chemie, EarlyView.Triply gated isomerization: In polar solvents, a phosphorus‐containing indirubin photoswitch undergoes visible‐light‐driven Z→E isomerization only when protonated, and reverts thermally via nucleophile‐catalyzed back‐isomerization. This three‐way control by light, acid, and nucleophile enables reversible photoisomerization.
Jacob Jan van der Wal +8 more
wiley +2 more sources