Geodesic
Testing isomorphism of central Cayley graphs over almost simple groups in polynomial time
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 154-180

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A Cayley graph over a group $G$ is said to be central if its connection set is a normal subset of $G$. It is proved that for any two central Cayley graphs over explicitly given almost simple groups of order $n$, the set of all isomorphisms from the first graph onto the second can be found in time $\mathrm{poly}(n)$. 
@article{ZNSL_2017_455_a12,
     author = {I. Ponomarenko and A. Vasil'ev},
     title = {Testing isomorphism of central {Cayley} graphs over almost simple groups in polynomial time},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {154--180},
     publisher = {mathdoc},
     volume = {455},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a12/}
}
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I. Ponomarenko; A. Vasil'ev. Testing isomorphism of central Cayley graphs over almost simple groups in polynomial time. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 154-180. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a12/