On one-point extensions of cluster-tilted algebras
  We define an operation which associates to a pair (B,M) where B is a cluster-tilted algebra and M is a B-module which lies in a local slice of B, a new cluster-tilted algebra B'. In terms of the quivers, this operation corresponds to adding one vertex (and arrows). 
Miki Oryu and Ralf Schiffler
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