A note on chain lengths and the Tutte polynomial

Ronald C. Read, Earl Glen Whitehead Jr.
2008 Discrete Mathematics  
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.
doi:10.1016/j.disc.2006.09.049 fatcat:zcumh3lbpbbclnoct7p6n67uvq