-1
$\begingroup$

When are the line graphs of Cayley graphs Cayley?

From this 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.

Improve this question
$\endgroup$
6
  • $\begingroup$ Why do you say "The question necessary includes the question of when a cayley graph is edge transitive. "? $\endgroup$
    – verret
    Commented Jul 6, 2020 at 21:33
  • $\begingroup$ @verret Is it just that in order for the line graph to be Cayley, it must at least be vertex transitive? And the vertices of the line graph are the edges of the graph. Or is there something more subtle that I am missing? $\endgroup$
    – Gordon Royle
    Commented Jul 7, 2020 at 0:03
  • $\begingroup$ @GordonRoyle yes, it is just as you said that the vertices of line graph correspond to edges of the graph itself, which made me think that my question includes the question of whether the graph is edge transitive $\endgroup$
    – vidyarthi
    Commented Jul 7, 2020 at 5:30
  • $\begingroup$ Sure, these graphs are a subclass of the class of edge-transitive Cayley graphs, but why is it necessary to solve the question for the larger class to understand the smaller class? Unless you have an actual reason for this, I suggest to remove it. $\endgroup$
    – verret
    Commented Jul 7, 2020 at 5:55
  • $\begingroup$ @verret edited. I thought it was somewhat easier to determine when a graph is edge transitive, so I added it $\endgroup$
    – vidyarthi
    Commented Jul 7, 2020 at 7:28

1 Answer 1

Reset to default
1
$\begingroup$

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).

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .