  These lecture notes are on automorphism groups of Cayley graphs and their
applications to optimal fault-tolerance of some interconnection networks. We
first give an introduction to automorphisms of graphs and an introduction to
Cayley graphs. We then discuss automorphism groups of Cayley graphs. We prove
that the vertex-connectivity of edge-transitive graphs is maximum possible. We
investigate the automorphism group and vertex-connectivity of some families of
Cayley graphs that have been considered for interconnection networks; we focus
on the hypercubes, folded hypercubes, Cayley graphs generated by
transpositions, and Cayley graphs from linear codes. New questions and open
problems are also discussed.
