Electronic Resource
Springer
Journal of algebraic combinatorics
10 (1999), S. 115-133
ISSN:
1572-9192
Keywords:
Tutte polynomial
;
chip-firing
;
critical group
;
growth function
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The 'dollar game' represents a kind of diffusion process on a graph. Under the rules of the game some cofigurations are both stable and recurrent, and these are known as critical cofigurations. The set of critical configurations can be given the structure of an abelian group, and it turns out that the order of the group is the tree-number of the graph. Each critical configuration can be assigned a positive weight, and the generating function that enumerates critical configurations according to weight is a partial evaluation of the Tutte polynomial of the graph. It is shown that the weight enumerator can also be interpreted as a growth function, which leads to the conclusion that the (partial) Tutte polynomial itself is a growth function.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018748527916
| Library |
Location |
Call Number |
Volume/Issue/Year |
Availability |
