What is and is not inside a Cayley graph?
Abstract
In this note we show that there is a cubic graph of girth 5 that is not a subgraph of any minimal Cayley graph. On the other hand, we show that any Generalized Petersen Graph G(n,k) with (n,k)=1 is an induced subgraph of a minimal Cayley graph. These results give insights into two comments of L\'aszl\'o Babai in [L. Babai, Automorphism groups, isomorphism, reconstruction. Graham, R. L. (ed.) et al., Handbook of combinatorics. Vol. 1-2, 1994].
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