Average Degree of Graphs Derived From The Ammann A2 Aperiodic Tiling
Xinyan Xu, Darren C. Ong
TL;DR
This paper derives a closed-form formula for the average degree of a graph constructed from the Ammann A2 aperiodic tiling, providing insights into its structural properties.
Contribution
It presents the first explicit formula for the average degree of graphs from Ammann A2 tilings, linking tiling geometry to graph theory.
Findings
Closed-form formula for average degree derived
Provides structural insights into Ammann A2 tiling graphs
Enhances understanding of aperiodic tiling properties
Abstract
The Ammann A2 tiling is a simple aperiodically ordered tiling of the plane. We consider the graph derived from this tiling, by treating each corner of each tile as a vertex and each side of each tile as an edge. We present a closed-form formula for the average degree of the graph corresponding to this Ammann A2 tiling.
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Taxonomy
TopicsCellular Automata and Applications · Quasicrystal Structures and Properties · DNA and Biological Computing