Timeline for Determinants in Graph Theory
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Sep 2, 2017 at 16:03 | history | suggested | Peter Heinig | CC BY-SA 3.0 |
The OP used the non-existant 'nonrecursive graph' for what is usually called 'loopless' in the graph-theoretic literature. Corrected. Also some other improvements.
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| Sep 2, 2017 at 15:38 | comment | added | Peter Heinig | I won't make this an answer since arguably this is not a property of the an adjacency matrix (rather of a pair consisting of a graph and a Pfaffian orientation, i.e., there is additional data involved), yet since the OP explicitly allowed "networks" (which are usually taken to subsume directed graphs), it is on-topic to mention: if you can give your graph a Pfaffian orientation, then the determinant of the corresponding signed adjacency matrix equals the square of the total number of perfect matchings. | |
| Sep 2, 2017 at 15:31 | review | Suggested edits | |||
| S Sep 2, 2017 at 16:03 | |||||
| Jun 27, 2013 at 13:37 | comment | added | Jeff Schenker | @Feliz and Jernej, thanks for pointing this out. you are of course correct. | |
| Jun 27, 2013 at 10:28 | answer | added | Adam Przeździecki | timeline score: 13 | |
| Jun 27, 2013 at 9:53 | comment | added | Felix Goldberg | @JeffSchenker As Jernej has pointed out, not the Laplacian itself, but any order $n-1$ principal sumbatrix thereof. | |
| Jun 27, 2013 at 9:23 | comment | added | Jernej | @JeffSchenker The determinant of the graph Laplacian is actually 0. | |
| Jun 27, 2013 at 9:12 | answer | added | Jernej | timeline score: 28 | |
| Jun 27, 2013 at 5:48 | comment | added | Gerry Myerson | You may be interested in Frank Harary, The determinant of the adjacency matrix of a graph, SIAM Review, Vol. 4, No. 3. (Jul., 1962), pp. 202-210, which I found at yaroslavvb.com/papers/harary-determinant.pdf If you have access to Math Reviews online, you might look for papers which cite this one. | |
| Jun 27, 2013 at 4:34 | comment | added | Jeff Schenker | This is not quite what you are asking, but the determinant of the graph Laplacian counts the number of spanning trees. This is known as Kirchhoff's matrix tree theorem: en.wikipedia.org/wiki/Kirchhoff's_theorem | |
| Jun 27, 2013 at 3:59 | review | First posts | |||
| Jun 27, 2013 at 4:27 | |||||
| Jun 27, 2013 at 3:43 | history | asked | Ion Georgiou | CC BY-SA 3.0 |