Abstract
Explicit formulas for coordination sequences of all 20 plane 2-uniform graphs are proved. The proof is based on the concept of layer-by-layer growth and on the canonical representation of geodesic chains in terms of special chains called as rays. The method works for a wide class of plane periodic graphs satisfying the following condition: for each sector of layer-by-layer growth there exists a graph vertex that is initial for two rays determining the sector. This generaizes the previous results where it is required that all vertices are initial for all rays.
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Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/zkri-2020-0002).
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Artikel in diesem Heft
- Frontmatter
- Graphical Synopsis
- Inorganic Crystal Structures
- Crystallographic orientation of ilmenite inclusions in amphibole – an electron backscatter diffraction study
- Quaternary intermetallics RE2Pt3Ga4In (RE=Y, Gd-Tm) – intergrowth structures of NdRh2Sn4 and TiNiSi related slabs
- Impact of the production method and diagnostics conditions on the compositions and structure of nanodimensional anatase
- Alkaline earth metal ordering in CaCu9Mg2 and SrCu9Mg2
- Elucidating the physical properties of the molybdenum oxide Mo4O11 and its tantalum substituted variant Mo2Ta2O11
- Coordination sequences of 2-uniform graphs
- Silicate-germanate K2Y[(Si3Ge)O10(OH)] with unusual complex corrugated layer and its correlation to ring silicate gerenite and chain silicate chkalovite
- Letter
- On the 80th birthday of Professor (retired) Dr. Dr. h.c. Peter Paufler
Artikel in diesem Heft
- Frontmatter
- Graphical Synopsis
- Inorganic Crystal Structures
- Crystallographic orientation of ilmenite inclusions in amphibole – an electron backscatter diffraction study
- Quaternary intermetallics RE2Pt3Ga4In (RE=Y, Gd-Tm) – intergrowth structures of NdRh2Sn4 and TiNiSi related slabs
- Impact of the production method and diagnostics conditions on the compositions and structure of nanodimensional anatase
- Alkaline earth metal ordering in CaCu9Mg2 and SrCu9Mg2
- Elucidating the physical properties of the molybdenum oxide Mo4O11 and its tantalum substituted variant Mo2Ta2O11
- Coordination sequences of 2-uniform graphs
- Silicate-germanate K2Y[(Si3Ge)O10(OH)] with unusual complex corrugated layer and its correlation to ring silicate gerenite and chain silicate chkalovite
- Letter
- On the 80th birthday of Professor (retired) Dr. Dr. h.c. Peter Paufler