Results 241 to 250 of about 13,317 (263)
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2020
Topological graph theory discusses, in most cases, graphs embedded in the plane (or other surfaces). For example, such plane graphs are sometimes regarded as the simplest town maps. Now, we consider a town having some pedestrian bridges, which cannot be realized by a plane graph. Its underlying graph can actually be regarded as a 1-plane graph.
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Topological graph theory discusses, in most cases, graphs embedded in the plane (or other surfaces). For example, such plane graphs are sometimes regarded as the simplest town maps. Now, we consider a town having some pedestrian bridges, which cannot be realized by a plane graph. Its underlying graph can actually be regarded as a 1-plane graph.
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Spectral extrema of 1-planar graphs
Discrete MathematicsA graph is \(1\)-planar if it can be drawn in the plane such that each of its edges is crossed at most once. The authors study the spectral radius (i.e., largest eigenvalue of the adjacency matrix) of \(1\)-planar graphs. Firstly, an upper bound \(5+\sqrt{2n+5}\) is given for the spectral radius of an \(n\)-vertex \(1\)-planar graph with \(n\ge 7 ...
Wenqian Zhang 0002 +2 more
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Fáry’s Theorem for 1-Planar Graphs
2012A plane graph is a graph embedded in a plane without edge crossings. Fary’s theorem states that every plane graph can be drawn as a straight-line drawing, preserving the embedding of the plane graph. In this paper, we extend Fary’s theorem to a class of non-planar graphs.
Seok-Hee Hong 0001 +3 more
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The 6-degeneracy of 1-planar graphs
Discrete Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingqin Wu +2 more
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Simple, reliable, and universal metrics of molecular planarity
Journal of Molecular Modeling, 2021Tian Lu
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Quantifying Planarity in the Design of Organic Electronic Materials
Angewandte Chemie - International Edition, 2021Yuxuan Che, Dmytro Perepichka
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Synchronized Planarity with Applications to Constrained Planarity Problems
ACM Transactions on Algorithms, 2023Simon Dominik Fink +2 more
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A Survey on Graph Drawing Beyond Planarity
ACM Computing Surveys, 2020Fabrizio Montecchiani +2 more
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Atomic Embeddability, Clustered Planarity, and Thickenability
Journal of the ACM, 2022Radoslav Fulek, Csaba Tóth
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On the Planarity of Graphs Associated with Symmetric and Pseudo Symmetric Numerical Semigroups
Mathematics, 2023Yongsheng Rao +2 more
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