One vertex spin-foams with the Dipole Cosmology boundary
  We find all the spin-foams contributing in the first order of the vertex expansion to the transition amplitude of the Bianchi-Rovelli-Vidotto Dipole Cosmology model. Our algorithm is general and provides spin-foams of arbitrarily given, fixed: boundary and, respectively, a number of internal vertices. We use the recently introduced Operator Spin-Network Diagrams framework. 
Marcin Kisielowski, Jerzy Lewandowski, Jacek Puchta
gr-qc hep-th