## Connective constants and height functions for Cayley graphs

The first author was supported in part by EPSRC Grant EP/I03372X/1. The second author was supported in part by Simons Collaboration Grant #351813 and NSF grant #1608896.

The first author was supported in part by EPSRC Grant EP/I03372X/1. The second author was supported in part by Simons Collaboration Grant #351813 and NSF grant #1608896.

The first author was supported in part by EPSRC Grant EP/I03372X/1. The second author was supported in part by Simons Collaboration Grant #351813 and NSF grant #1608896.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

We give the classification of all (minimal) Cayley bipartite or perfect finite groups as well as finite graphs $Gamma$ for which there are only finitely many (minimal) Cayley $Gamma$-free groups.

Topologies for data center interconnection networks have been proposed in the literature through various graph classes and operations. A common trait to most existing designs is that they enhance the symmetric properties of the underlying graphs. Indeed, symmetry is a desirable property for interconnection networks because it minimizes congestion p...

Topologies for data center interconnection networks have been proposed in the literature through various graph classes and operations. A common trait to most existing designs is that they enhance the symmetric properties of the underlying graphs. Indeed, symmetry is a desirable property for interconnection networks because it minimizes congestion p...