This paper gives a generalized description of fat tree topology, and invented the notation:

\[XGFT(h;m_1,m_2, ..., m_h; w_1, w_2, ..., w_h)\]

This notation means the fat tree has height \(h\), and on level \(i\) (\(0\le i\le h-1\)) each node has \(w_{i+1}\) parent nodes and \(m_i\) children nodes. Level 0 is the bottom-most layer, so assumed \(m_0=0\). So for the degree-3 fat-tree that I always use, it can be expressed by \(XGFT(3;3,3,6;1,3,3)\).

Bibliographic data

   title = "On Generalized Fat Trees",
   author = "Sabine R. Öhring and Maximilian Ibel and Sajal K. Das and Mohan J. Kumar",
   booktitle = "Proc. 9th International Parallel Processing Symposium",
   Mon = "Apr",
   pages = "37--44",
   address = "Santa Barbara, CA",
   year = "1995",