Results 41 to 50 of about 14,901,088 (199)
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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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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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) $\sum_{x\in N^{-}(v)}f(x)\ge k ...
N. Dehgard, L. Volkmann
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Dominating the Direct Product of Two Graphs through Total Roman Strategies
Mathematics, 2020 Given a graph G without isolated vertices, a total Roman dominating function for G is a function f:V(G)→{0,1,2} such that every vertex u with f(u)=0 is adjacent to a vertex v with f(v)=2, and the set of vertices with positive labels induces a graph of ...
Abel Cabrera Martínez +3 more
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Halogen Surface Terminations in Ti3C2 MXenes for Interface Engineering in Perovskite Solar Cells
Advanced Materials Interfaces, EarlyView.Controlled halogen surface terminations in Ti3C2${\rm Ti}_3{\rm C}_2$ MXenes enable the isolation of structure‐property relationships, revealing how –Cl and –Br terminations influence interlayer spacing, electronic behavior, and work function. When incorporated into IT‐4F‐based interfacial layers, these MXenes modulate interfacial processes and device ...
Morgana Müller de França +10 more
wiley +1 more source
Total Roman Domination of Kneser Graphs
, 2023 The total Roman domination number of a graph is the smallest possible sum of the weights 0, 1, and 2 applied to vertices of the graph that satisfy certain rules originating from Roman military strategy.
Stainsby, Cole +6 more
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Total roman domination in digraphs
, 2021 Let D be a nite and simple digraph with vertex set V (D). A Roman dominating function (RDF) on a digraph D is a function f : V (D) → {0; 1; 2} satisfying the condition that every vertex v with f(v) = 0 has an in-neighbor u with f(u) = 2. The weight of an
Zhuang, Wei, Hu, Kangxiu, Hao, Guoliang
core
Smart Antibacterial Coatings: Harnessing Bacterial Redox Activity for Infection Control
Advanced Materials Interfaces, EarlyView.In this study, we have shown that ceftazidime‐loaded poly(3,4‐ethylenedioxythiophene) (PEDOT@CAZ) functions as a smart, redox‐responsive antibacterial coating that couples bacterial electrical activity with localized antibiotic delivery. Shewanella oneidensis and Pseudomonas aeruginosa induced distinct redox responses in PEDOT, reflecting their ...
Abdullah +8 more
wiley +1 more source
Nonnegative signed total Roman domination in graphs
Communications in Combinatorics and Optimization, 2020 Let $G$ be a finite and simple graph with vertex set $V(G)$. A nonnegative signed total Roman dominating function (NNSTRDF) on a graph $G$ is a function $f:V(G)\rightarrow\{-1, 1, 2\}$ satisfying the conditions that (i) $\sum_{x\in N(v)}f(x)\ge 0$ for
Nasrin Dehgardi, Lutz Volkmann
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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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