Timeline for Product of geodesic distances
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 30, 2014 at 19:54 | comment | added | Rob Richmond | I've been playing around a bit more with specific structures and using your Mathematica code to check the example graphs. Distance-transitive graphs may be a promising class en.wikipedia.org/wiki/Distance-transitive_graph . | |
| Jun 30, 2014 at 18:48 | comment | added | Rob Richmond | The Dyck graph is particularly illustrative as it is one that I would have intuitively thought would have my property. Would you or Gabriel mind sharing a sketch of the proof for Kneser and cycle graphs? My cycle graph proof is really messy and doesn't point at all towards constraints I may be able to impose. | |
| Jun 28, 2014 at 11:17 | comment | added | Adam P. Goucher | Actually, arc-transitivity isn't enough, either; the Dyck graph lacks your property (and has just 32 vertices). | |
| Jun 28, 2014 at 11:06 | comment | added | Adam P. Goucher | Well, the counter-example shows that vertex-transitivity is not enough. My friend and colleague Gabriel Gendler proved that Kneser graphs and cycle graphs have your property, so maybe arc-transitivity suffices. en.wikipedia.org/wiki/Arc-transitive_graph | |
| Jun 27, 2014 at 21:52 | comment | added | Rob Richmond | Thanks for the counter example, this is useful. Do you have any intuition of what sort of structure I could impose on graphs for this property to hold? | |
| Jun 27, 2014 at 21:51 | vote | accept | Rob Richmond | ||
| Jun 27, 2014 at 16:18 | history | answered | Adam P. Goucher | CC BY-SA 3.0 |