A Polynomial Delay Algorithm for Generating Connected Induced Subgraphs   of a Given Cardinality
  We give a polynomial delay algorithm, that for any graph $G$ and positive integer $k$, enumerates all connected induced subgraphs of $G$ of order $k$. Our algorithm enumerates each subgraph in at most $O((k\min\{(n-k),k\Delta\})^2(\Delta+\log k))$ and uses linear space $O(n+m)$, where $n$ and $m$ are respectively the number of vertices and edges of $G$ and $\Delta$ is the maximum degree. 
Khaled Elbassioni
cs.DS