An Isoperimetric Problem in Cayley Graphs

Abstract.

Let T be a minimal generating subset of a group G . Let Γ be the Cayley graph defined on G by $S=T\cup T^{-1}$ . Let d ₂ be the minimal cardinality of the boundary of two points. We show that, for |S|>4 , every cutset with cardinality less than d ₂ must isolate a single vertex.