Generalization of the Bollob\'as-Riordan polynomial for tensor graphs

Understand

Tensor models are used nowadays for implementing a fundamental theory of quantum gravity.

• We define here a polynomial $\mathcal T$ encoding the supplementary topological information.
• This polynomial is a natural generalization of the Bollob\'as-Riordan polynomial (used to characterize matrix graphs) and is different of the Gur\uau polynomial, (R.
• Gur\uau, "Topological Graph Polynomials in Colored Group Field Theory", Annales Henri Poincare {\bf 11}, 565-584 (2010)) defined for a particular class of tensor graphs, the colorable ones.