On terminal forms for topological polynomials for ribbon graphs: The $N$petal flower
Abstract
The BollobasRiordan polynomial [Math. Ann. 323, 81 (2002)] extends the Tutte polynomial and its contraction/deletion rule for ordinary graphs to ribbon graphs. Given a ribbon graph $\cG$, the related polynomial should be computable from the knowledge of the terminal forms of $\cG$ namely specific induced graphs for which the contraction/deletion procedure becomes more involved. We consider some classes of terminal forms as rosette ribbon graphs with $N\ge 1$ petals and solve their associate BollobasRiordan polynomial. This work therefore enlarges the list of terminal forms for ribbon graphs for which the BollobasRiordan polynomial could be directly deduced.
 Publication:

arXiv eprints
 Pub Date:
 December 2012
 arXiv:
 arXiv:1212.5961
 Bibcode:
 2012arXiv1212.5961A
 Keywords:

 Mathematics  Combinatorics;
 05C10;
 57M15
 EPrint:
 18 pages, 8 figures