Int. J. Topol., Volume 1, Issue 1 (September 2024) – 1 article

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Article
Embeddings of Graphs: Tessellate and Decussate Structures
by Michael O’Keeffe and Michael M. J. Treacy
Int. J. Topol. 2024, 1(1), 1-10; https://doi.org/10.3390/ijt1010001 - 29 Mar 2024
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Abstract
We address the problem of finding a unique graph embedding that best describes a graph’s “topology” i.e., a canonical embedding (spatial graph). This question is of particular interest in the chemistry of materials. Graphs that admit a tiling in 3-dimensional Euclidean space are [...] Read more.
We address the problem of finding a unique graph embedding that best describes a graph’s “topology” i.e., a canonical embedding (spatial graph). This question is of particular interest in the chemistry of materials. Graphs that admit a tiling in 3-dimensional Euclidean space are termed tessellate, those that do not decussate. We give examples of decussate and tessellate graphs that are finite and 3-periodic. We conjecture that a graph has at most one tessellate embedding. We give reasons for considering this the default “topology” of periodic graphs. Full article
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