Open Problem Garden - Cores of Cayley graphs - Comments

Who first conjectured this? (re: Cores of Cayley graphs)

Anonymous — Wed, 29 Feb 2012 12:59:17 +0100

Who first conjectured that the core of a cubelike graph is cubelike?

Re: Question needs refining... (re: Cores of Cayley graphs)

Robert Samal — Sat, 01 Mar 2008 03:09:22 +0100

That is true. I was mainly thinking about (for a prime ). However, your suggestion (b) looks sensible as well.

Thanks for your comment!

Robert Samal

Question needs refining... (re: Cores of Cayley graphs)

Gordon Royle — Fri, 22 Feb 2008 21:48:11 +0100

As stated, the conjecture is false in an uninteresting way ... it is possible for a Cayley graph of Z_15 have a 5-cycle as a core.... So if we take M = Z_15 then the result is false.

Perhaps the question should either (a) be restricted to elementary abelian groups or (b) have the conclusion being that the core of a Cayley graph on M must be a Cayley graph on N where N is a (group) homomorphic image of M.

Gordon Royle http://people.csse.uwa.edu.au/gordon

Cores of Cayley graphs

Robert Samal — Tue, 06 Mar 2007 22:37:06 +0100

Author(s): Samal

Subject: Graph Theory » Coloring » Homomorphisms

Conjecture Let be an abelian group. Is the core of a Cayley graph (on some power of ) a Cayley graph (on some power of )?