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Dima Pasechnik
Dima Pasechnik
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As soon as the generating set of a Cayley graph of a group $G$ is a union of conjugacy classes of $G$, the graph lives in the commutative association scheme of these classes, where the multiplication is determined by the character table of $G$. Thus things like diameter, eigenvalues, can be determined from the character table, although this is not necessarily trivial.

Just for fun, I computed the eigenvalues of this graph for $G=A_n$, $n=15$, and they are all integers. Not sure if this is easy to explain...

As soon as the generating set of a Cayley graph of a group $G$ is a union of conjugacy classes of $G$, the graph lives in the commutative association scheme of these classes, where the multiplication is determined by the character table of $G$. Thus things like diameter, eigenvalues, can be determined from the character table, although this is not necessarily trivial.

As soon as the generating set of a Cayley graph of a group $G$ is a union of conjugacy classes of $G$, the graph lives in the commutative association scheme of these classes, where the multiplication is determined by the character table of $G$. Thus things like diameter, eigenvalues, can be determined from the character table, although this is not necessarily trivial.

Just for fun, I computed the eigenvalues of this graph for $G=A_n$, $n=15$, and they are all integers. Not sure if this is easy to explain...

Source Link
Dima Pasechnik
Dima Pasechnik
  • 14k
  • 2
  • 34
  • 70

As soon as the generating set of a Cayley graph of a group $G$ is a union of conjugacy classes of $G$, the graph lives in the commutative association scheme of these classes, where the multiplication is determined by the character table of $G$. Thus things like diameter, eigenvalues, can be determined from the character table, although this is not necessarily trivial.