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Topological densities of periodic graphs

  • Anton Shutov and Andrey Maleev
Published/Copyright: November 25, 2020
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Zeitschrift für Kristallographie - Crystalline Materials
From the journal Zeitschrift für Kristallographie - Crystalline Materials Volume 235 Issue 12

Abstract

We propose a new method to calculate topological densities of periodic graphs based on the concept of layer-by-layer growth. Topological density is expressed in terms of metric characteristics: the volume of the fundamental domain and the volume of the growth polytope of the graph. Our method is universal (works for all d-periodic graphs) and is easily automated. As examples, we calculate topological densities of all 20 plane 2-uniform graphs and 14 carbon allotrope modifications.

Keywords: layer-by-layer growth; periodic graph; topological density
Corresponding author: Anton Shutov, Vladimir State University, Gorky Street, 87, Vladimir, 600000, Russian Federation, E-mail:

Unfortunately, Andrey Maleev passed away in November, 2020.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-07-06
Accepted: 2020-10-12
Published Online: 2020-11-25
Published in Print: 2020-12-16

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Graphical Synopsis
  3. Original Papers
  4. Crystal structure relations in the binary system Li–Sn including the compound c-Li3Sb
  5. γ-Brass type structures with I- and P-cell in the ternary Cu–Zn–In system
  6. Halogen bonding in crystals of free 1,2-diiodo-ethene (C2H2I2) and its π-complex [CpMn(CO)2](π-C2H2I2)
  7. Topological densities of periodic graphs
https://doi.org/10.1515/zkri-2020-0065
Keywords for this article
layer-by-layer growth; periodic graph; topological density

Articles in the same Issue

  1. Frontmatter
  2. Graphical Synopsis
  3. Original Papers
  4. Crystal structure relations in the binary system Li–Sn including the compound c-Li3Sb
  5. γ-Brass type structures with I- and P-cell in the ternary Cu–Zn–In system
  6. Halogen bonding in crystals of free 1,2-diiodo-ethene (C2H2I2) and its π-complex [CpMn(CO)2](π-C2H2I2)
  7. Topological densities of periodic graphs
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