Multi-graviton theory in vierbein formalism
  Recently, multi-graviton theory on a simple closed circuit graph corresponding to the $S^1$ compactification of the Kaluza-Klein (KK) theory has been considered. In the present paper, we extend this theory to that on a general graph and study what modes of particles are included. Furthermore, we generalize it in a possible non-linear theory based on the vierbein formalism and study cosmological solutions. 
Teruki Hanada, Kazuhiko Shinoda and Kiyoshi Shiraishi (Yamaguchi   University)