  The Bollobas-Riordan 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 Bollobas-Riordan polynomial. This work
therefore enlarges the list of terminal forms for ribbon graphs for which the
Bollobas-Riordan polynomial could be directly deduced.
