Highly Symmetric Expanders

Expander graphs are relevant to theoretical computer science in addition to the construction of high-performance switching networks. In communication network applications, a high degree of symmetry in the underlying topology is often advantageous, as it may reduce the complexity of designing and analyzing switching and routing algorithms. We give explicit constructions of expander graphs that are highly symmetric. In particular, we construct infinite families of Ramanujan graphs with large guarantees on the orders of their automorphism groups. Although nonlinear, our expander graphs are within a constant factor of the size of the smallest graphs exhibiting the same expansion properties. This work generalizes and extends in several directions a previous explicit construction of expander graphs based on finite projective spaces due to Alon.