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A note on chain lengths and the Tutte polynomial

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
308
Issue
10
Identifiers
DOI: 10.1016/j.disc.2006.09.049
Keywords
  • Tutte Polynomial
  • Homeomorphic Graphs
  • Tutte-Equivalent Graphs
  • Tutte-Unique Graphs
  • [Formula Omitted]-Theta-Graphs

Abstract

Abstract We show that the number of chains of given length in a graph G can be easily found from the Tutte polynomial of G . Hence two Tutte-equivalent graphs will have the same distribution of chain lengths. We give two applications of this latter statement. We also give the dual results for the numbers of multiple edges with given muliplicities.

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