The coordination sequence s(k) of a graph 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. A possible application to the theory of critical phenomena in lattice models is outlined.
Zeitschrift fur Kristallographie
- Pub Date:
- January 1997
- Condensed Matter - Statistical Mechanics;
- Mathematics - Combinatorics
- 8 pages, LaTeX, 1 Postscript figure included, using epsf.sty and amssymb.sty