Recipe theorems for polynomial invariants on ribbon graphs with   half-edges
  We provide recipe theorems for the Bollob\`as and Riordan polynomial $\mathcal{R}$ defined on classes of ribbon graphs with half-edges introduced in arXiv:1310.3708[math.GT]. We also define a generalized transition polynomial $Q$ on this new category of ribbon graphs and establish a relationship between $Q$ and $\mathcal{R}$. 
Remi C. Avohou, Joseph Ben Geloun and Mahouton N. Hounkonnou
math.CO