Coordination sequences for root lattices and related graphs
- 1 April 1997
- journal article
- Published by Walter de Gruyter GmbH in Zeitschrift für Kristallographie - Crystalline Materials
- Vol. 212 (4), 253-256
- https://doi.org/10.1524/zkri.1997.212.4.253
Abstract
The coordination sequence s Λ(k) of a graph Λ counts the number of its vertices which have distance k from a given vertex, where the distance between two vertices is defined as the minimal number of bonds in any path connecting them. For a large class of graphs, including in particular the classical root lattices, we present the coordination sequences and their generating functions, summarizing and extending recent results of Conway and Sloane [1].Keywords
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