Timeline for Algebraic connectivity of the path $P_n$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 21, 2019 at 7:02 | comment | added | Martin Rubey | It is Lemma 2.10 on page 69 of my diploma thesis (mat.univie.ac.at/~kratt/theses/rubey.ps.gz), but I am not sure whether you want to reference that. Unfortunately, I did not know that \cite is an important thing to do back then, but I can check tomorrow whether one of the references fit. (F.T. Boesch, H. Prodinger does not contain it, unfortunately) | |
| Jul 20, 2019 at 11:44 | comment | added | Ivan Feshchenko | I would like to have a reference to a simple direct proof (as my proof, where I need to know only characteristic polynomial of the adjacency matrix of the path, in terms of the Chebyshev polynomials of the second kind) published in article or book. | |
| Jul 19, 2019 at 22:41 | comment | added | Fedor Petrov | Do you need the reference to any proof or to the first published proof ever? You may take the proof say here ocw.mit.edu/courses/mathematics/… if you need a book I would check that of C. Godsil, G. F. Royle (Algebraic graph theory) or Fan R. K. Chung (Spectral graph theory) | |
| Jul 19, 2019 at 21:02 | comment | added | Ivan Feshchenko | [6] R. Grone, R.Merris, The Laplacian spectrum of a graph II, 1994. I did not find the result on the algebraic connectivity of the path in the paper. | |
| Jul 19, 2019 at 20:45 | comment | added | Ivan Feshchenko | They refer to the paper of Fiedler: M. Fiedler, Algebraic connectivity of graphs, 1973. But there is NO proof in the paper of Fiedler. | |
| Jul 19, 2019 at 20:35 | comment | added | Ivan Feshchenko | [5] R. Grone, R. Merris, V.S.Sunder, The Laplacian spectrum of a graph. | |
| Jul 19, 2019 at 19:46 | comment | added | Fedor Petrov | here sciencedirect.com/science/article/pii/… it is claimed that the papers [5,6] contain what you need | |
| Jul 19, 2019 at 17:11 | history | asked | Ivan Feshchenko | CC BY-SA 4.0 |