Some remarks on iterated line graphs on Cayley graphs

Abstract

This article investigates the properties of iterated line graphs derived from Cayley graphs of finitely generated groups. We study their graph-theoretical properties such as diameter and automorphism groups, and present recursive algorithms for their construction. We show that while these iterated graphs preserve certain algebraic properties, their size grows exponentially and their diameters grow linearly. A generalization of Whitney's theorem about the automorphism groups is presented.