Results 41 to 50 of about 86,729 (238)
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
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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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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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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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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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
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
doaj +1 more source
Portraits, Power, and Patronage in the Late Roman Republic [PDF]
, 2000 Recent work in ancient art history has sought to move beyond formalist interpretations of works of art to a concern to understand ancient images in terms of a broader cultural, political, and historical context.
Tanner, J
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Mapping Nanoscale Buckling in Atomically Thin Cr2Ge2Te6
Advanced Functional Materials, EarlyView.Atomic‐resolution STEM is used to resolve nanoscale buckling in monolayer Cr2Ge2Te₆. A noise‐robust image analysis reconstructs three‐dimensional lattice distortions from single plan‐view images, revealing pronounced defect‐driven nm‐scale out‐of‐plane buckling.
Amy Carl +20 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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