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Coordination sequences of 2-uniform graphs

  • Anton Shutov und Andrey Maleev EMAIL logo
Veröffentlicht/Copyright: 18. April 2020

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).


Received: 2020-01-14
Accepted: 2020-03-13
Published Online: 2020-04-18
Published in Print: 2020-05-26

©2020 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 30.1.2026 von https://www.degruyterbrill.com/document/doi/10.1515/zkri-2020-0002/pdf
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