Topological densities of periodic graphs
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Anton Shutov
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.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Graphical Synopsis
- Original Papers
- Crystal structure relations in the binary system Li–Sn including the compound c-Li3Sb
- γ-Brass type structures with I- and P-cell in the ternary Cu–Zn–In system
- Halogen bonding in crystals of free 1,2-diiodo-ethene (C2H2I2) and its π-complex [CpMn(CO)2](π-C2H2I2)
- Topological densities of periodic graphs
Artikel in diesem Heft
- Frontmatter
- Graphical Synopsis
- Original Papers
- Crystal structure relations in the binary system Li–Sn including the compound c-Li3Sb
- γ-Brass type structures with I- and P-cell in the ternary Cu–Zn–In system
- Halogen bonding in crystals of free 1,2-diiodo-ethene (C2H2I2) and its π-complex [CpMn(CO)2](π-C2H2I2)
- Topological densities of periodic graphs
