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Petersen graph is this graph:

enter image description here

Petersen graph can not be a Cayley graph.

How to prove that?

Can someone give a general method to judge a graph is or not a Cayley graph?

VividD
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gaoxinge
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    check this out http://math.stackexchange.com/questions/348779/petersen-graph-is-not-a-cayley-graph?rq=1 – hbm Feb 20 '14 at 04:59
  • @hbm Why does $|S|=3$? I think $S={a_1,a_2}$ and $a_1^2=1,a_2^2\ne 1$. Then every vertex has three neighborhoods and satisfies the question. – gaoxinge Feb 20 '14 at 05:33
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    the graph is $|S|$-regular. – hbm Feb 20 '14 at 05:37
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    See here http://exwiki.org/mw/index.php?title=The_Petersen_graph_is_not_a_Cayley_graph – Jernej Feb 20 '14 at 15:23

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