Timeline for Graphs with a unique transmission value
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2012 at 3:04 | history | edited | Gordon Royle | CC BY-SA 3.0 |
added 1020 characters in body
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| Nov 28, 2012 at 1:58 | comment | added | Gordon Royle | @Brendan: easy to go higher, but I should be marking and writing papers and grant applications, not getting sidetracked by appealing MO problems :-(. | |
| Nov 27, 2012 at 22:46 | comment | added | Brendan McKay | @gordon-royle: Try larger sizes for almost-regular graphs, you'll be able to go further. For example "geng -d6D7 12" only takes 30 sec. | |
| Nov 27, 2012 at 19:26 | comment | added | Harry Altman | For those wondering what this graph looks like: Take 3 copies of the diamond graph and glue them together at the degree-2 vertices so as to form a triangle. | |
| Nov 27, 2012 at 15:22 | comment | added | Felix Goldberg | I ran lots of random graphs but found none; probably my parameters were not good... | |
| Nov 27, 2012 at 14:18 | comment | added | Gordon Royle | This was a 3-second computer search. Or rather, I already had Brendan's program to generate the graphs and a program implementing Floyd's all-pairs-shortest paths algorithm. So all I had to write was something to check the row sums. Interestingly there are no non-regular examples on 10 vertices. I think Brendan's comment about cartesian product is correct, so there's no limit on diameter or non-regularity. It would still be interesting to see if these are special in any way; the example above has only 4 distinct eigenvalues, which may be relevant. | |
| Nov 27, 2012 at 11:15 | comment | added | Felix Goldberg | Gordon, thanks for the nice example. I had a feeling there had to be one! Did you find it in some "smart" way or by search? | |
| Nov 27, 2012 at 2:46 | history | answered | Gordon Royle | CC BY-SA 3.0 |