I have two questions about Cayley graphs. Any answers will be appreciate.


1) Do we have any Cayley graph that has Petersen graph as its induced subgraph?


2) Suppose $Cay(G,S)$ be a Cayley graph that $G$ is a finite group. Can we characterize any induced subgraphs of $Cay(G,S)$?


Thanks for any answer and guidance. 



Cayley graphs and its subgraphs
If $X$ is a vertex-transitive graph and the stabilizer of a vertex has order $m$, then the lexicographic product of $K\_m$ by $X$ is a Cayley graph. We get the lexicographic product here by replacing each vertex of $X$ by $K\_m$ and, where two vertices of $X$ are adjacent, join
each vertex in one $K\_m$ to each vertex in the other. So this product contains copies of $X$ as
an induced subgraph and is a Cayley graph for $Aut(X)$. The result and the construction are due to Sabidussi.


You second question is too vague to admit an answer. 


