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

@inproceedings{
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",
}