When are the line graphs of Cayley graphs Cayley?


From [this](https://mathoverflow.net/questions/150744/the-line-graphs-of-complete-graphs-and-cayley-graphs) link we can know when the line graphs of complete graphs are cayley. But, my question pertains to the larger class of Cayley graphs. Are there new results in this direction? Any hints? Thanks beforehand.



Which line graphs of Cayley graphs are Cayley
One would expect few Cayley graphs to have this property, as their automorphism group is just not big enough. Either way, a complete classification is almost certainly out of reach. Even the example you give of complete graphs is far from trivial (the published proof requires on quite a few group-theoretic results, including the Feit-Thompson Theorem).


