Cayley or not Cayley? And if not Cayley "then what"?

Simone Severini · science forum beginner Joined: 13 Mar 2005 Posts: 16

Dear All,

I have a cubic graph on 60 vertices whose automorphism group has order
120, it is 1-transitive and it is generated by the two elements

a =
(2,5)(3,4)(6,21)(7,25)(8,24)(9,23)(10,22)(11,16)(12,20)(13,19)(14,1 Cool

(15,17)(26,32)(27,31)(28,35)(29,34)(30,33)(36,47)(37,46)(38,50)(39,49)(40,4 Cool

(41,42)(43,45)(51,52)(53,55)(56,5 Cool

(59,60)

b =
(1,22,26,48,55,44,38,14,7,5 Cool

(2,21,27,47,51,43,39,13,8,59)(3,25,28,46,52,42,40,12,9,60)(4,24,29,50,53,41,36,11,10,56)(5,23,30,49,54,45,37,15,6,57)(16,31,17,35,18,34,19,33,20,32)

Is this some known graph?

Is it a Cayley graph? (I don't know how to find out about this. I guess
I should check if there is a regular subgroup of the aut. group. Well,
I don't know.) Is it trivial to find out this from the numbers above
(60, 120)?

In case, I have got the adj. matrix in mat format downloadable from

http://www-users.york.ac.uk/~ss54/reidun1.mat

Thanks a lot for your time...

Simone
http://www-users.york.ac.uk/~ss54

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