Timeline for How can I prove that a particular family of graphs is integral?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 1, 2014 at 19:01 | vote | accept | jamisans | ||
| Mar 1, 2014 at 15:40 | answer | added | David E Speyer | timeline score: 15 | |
| Feb 28, 2014 at 23:24 | comment | added | Eckhard | The eigenvectors appear to be integral of small magnitude and containing lots of zeros. | |
| Feb 28, 2014 at 22:35 | comment | added | Jernej | It appears that all the graphs are vertex-transitive. If this is indeed so you could try to apply the results from link.springer.com/article/10.1007%2FBF02018821#page-1 or even sciencedirect.com/science/article/pii/0095895679900790 | |
| Feb 28, 2014 at 22:17 | history | edited | jamisans | CC BY-SA 3.0 |
Added another example
|
| Feb 28, 2014 at 21:54 | answer | added | Igor Rivin | timeline score: 2 | |
| Feb 28, 2014 at 21:52 | comment | added | jamisans | Perhaps $G_{3,k}$ is the line graph of $K_{k,k,k}$. Also if $n>3$ the (presumed) smallest eigenvalue of $1-n$ would be less than -2, which means that $G_{n,k}$ couldn't be a line graph. | |
| Feb 28, 2014 at 21:41 | comment | added | F. C. | sage says that G(3,3), G(3,2), G(4,2), G(4,3) and G(3,4) are not Cartesian products. And also that G(3,3), G(3,4) and G(3,5) are also line graphs. | |
| Feb 28, 2014 at 21:24 | answer | added | F. C. | timeline score: 4 | |
| Feb 28, 2014 at 21:02 | comment | added | jamisans | Thanks. I know at least the displayed graph is not a cartesian product of smaller graphs. It does end up being the line graph of the octahedral graph, however. I will start to look at some other cases to see if they can be decomposed. | |
| Feb 28, 2014 at 20:05 | comment | added | Jernej | Can you express them as smaller graphs with a given operation? For example are they ever Cartesian product graphs? Nice construction BTW. | |
| Feb 28, 2014 at 19:52 | comment | added | jamisans | I haven't looked at eigenvectors yet - I'll start to do that and see if I can learn anything. | |
| Feb 28, 2014 at 19:38 | comment | added | Alex Degtyarev | Do the examples you've done help you guess the eigenvectors? | |
| Feb 28, 2014 at 19:29 | history | asked | jamisans | CC BY-SA 3.0 |