Distance sequences and percolation thresholds in Archimedean tilings

✍ Scribed by P. Préa

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 240 KB
• Volume: 26
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(97)00216-1

✦ Synopsis

Given a graph G, a vertex x of G, and an integer n 2 0, the circle C, of center x and of radius n is the set of all the vertices at distance n from x, and the circumference cn is the cardinality of C,,. The distance sequence of G and center x is the sequence (co, ~1, ~2,. . , b,. . ). When G is vertex-t,ransitive, we can talk about the distance sequence of G. In this note, we give formulae for calculating distance sequences in Archimedean tilings (which can be seen as vertex-transitive graphs) and we can see that, for these tilings, these sequences are linked with the percolation thresholds.