Journal
SIAM JOURNAL ON DISCRETE MATHEMATICS
Volume 30, Issue 2, Pages 1046-1057Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1024615
Keywords
Tutte polynomial; connected graphs
Categories
Funding
- ARC DECRA grant
- ARC grant
- NSFC grant [61170301]
- NSF China Research Fellowship for International Young Scientists [11450110409, 11550110491]
- AARMS
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Let c(n) denote the number of vertex-labeled connected graphs on n vertices. Using group actions and elementary number theory, we show that the infinite sequence, c(n) : n >= 1, is ultimately periodic modulo every positive integer. We state and prove our results for sequences defined by a weighted generalization of c(n) and conjecture that these results are suggestive of similar periodic behavior of the Tutte polynomial evaluations of the complete graph K-n at integer points.
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