Results 51 to 60 of about 59,758 (255)
Cartesian Products of Graphs and Metric Spaces
European Journal of Combinatorics, 2000 The authors give a short proof of the known fact that decomposition of a connected graph into a cartesian product of indecomposable factors is unique up to isomorphism. They then present a generalization of the results which shows uniqueness of decomposition for a wide class of product operations on general finite metric spaces.
Avgustinovich, S., Fon-Der-Flaass, D.
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The Thickness of Amalgamations and Cartesian Product of Graphs
Discussiones Mathematicae Graph Theory, 2017 The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been ...
Yang Yan, Chen Yichao
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Weak k-reconstruction of cartesian product graphs
Electronic Notes in Discrete Mathematics, 2001 By Ulam's conjecture every finite graph ▫$G$▫ can be reconstructed from its deck of vertex deleted subgraphs. The conjecture is still open, but many special cases have been settled. In particular, one can reconstruct Cartesian products. We consider the case of ▫$k$▫-vertex deleted subgraphs of Cartesian products and prove that one can decide whether a ...
Imrich, Wilfried +2 more
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Power domination of the cartesian product of graphs
AKCE International Journal of Graphs and Combinatorics, 2016 In this paper, we first give a brief survey on the power domination of the Cartesian product of graphs. Then we conjecture a Vizing-like inequality for the power domination problem, and prove that the inequality holds when at least one of the two graphs ...
K.M. Koh, K.W. Soh
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Some Results on Palette Index of Cartesian Product Graphs
Mathematical Problems of Computer Science, 2021 Given a proper edge coloring α of a graph G, we define the palette SG(ν, α) of a vertex ν ∈ V (G) as the set of all colors appearing on edges incident to ν. The palette index š(G) of G is the minimum number of distinct palettes occurring in a proper edge
Khachik S. Smbatyan
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Clean Up Behind You ‐ Novel Patterning Approach for Solid Immersion Lenses
Advanced Functional Materials, EarlyView.A focused ion beam (FIB) milling strategy enables rapid fabrication of solid immersion lenses (SILs) with smooth, debris‐free surfaces eliminating the need for post‐processing. The optimized pattern improves efficiency and surface quality. SILs containing NV centers are also investigated, confirming the technique's suitability for quantum and photonic ...
Aleksei Tsarapkin +10 more
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Eccentric Harmonic Index for the Cartesian Product of Graphs
Journal of Mathematics, 2022 Suppose ρ is a simple graph, then its eccentric harmonic index is defined as the sum of the terms 2/ea+eb for the edges vavb, where ea is the eccentricity of the ath vertex of the graph ρ. We symbolize the eccentric harmonic index (EHI) as He=Heρ.
Kamel Jebreen +5 more
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On Linkedness of Cartesian Product of Graphs [PDF]
, 2014 We study linkedness of Cartesian product of graphs and prove that the product of an $a$-linked and a $b$-linked graphs is $(a+b-1)$-linked if the graphs are sufficiently large. Further bounds in terms of connectivity are shown. We determine linkedness of
Meszaros, Gabor
core
Asymptotics of the Euler number of bipartite graphs
, 2007 We define the Euler number of a bipartite graph on $n$ vertices to be the number of labelings of the vertices with $1,2,...,n$ such that the vertices alternate in being local maxima and local minima.
Ehrenborg +4 more
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Generative Models for Crystalline Materials
Advanced Materials, EarlyView.Generative machine learning models are increasingly used in crystalline materials design. This review outlines major generative approaches and assesses their strengths and limitations. It also examines how generative models can be adapted to practical applications, discusses key experimental considerations for evaluating generated structures, and ...
Houssam Metni +15 more
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