| Title:
|
Constructions for type I trees with nonisomorphic Perron branches (English) |
| Author:
|
Kirkland, Steve |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
617-632 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections between characteristic vertices, algebraic connectivity, and Perron values of certain positive matrices associated with the tree. (English) |
| MSC:
|
05C05 |
| MSC:
|
05C50 |
| MSC:
|
15A09 |
| idZBL:
|
Zbl 1003.05070 |
| idMR:
|
MR1708342 |
| . |
| Date available:
|
2009-09-24T10:25:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127514 |
| . |
| Reference:
|
[1] M. Fiedler: Algebraic connectivity of graphs.Czechoslovak Math. J. 23 (98) (1973), 298–305. Zbl 0265.05119, MR 0318007 |
| Reference:
|
[2] M. Fiedler: A property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory.Czechoslovak Math. J. 25 (100) (1975), 619–633. MR 0387321 |
| Reference:
|
[3] R. Grone and R. Merris: Algebraic connectivity of trees.Czechoslovak Math. J. 37 (112) (1987), 660–670. MR 0913997 |
| Reference:
|
[4] S. Kirkland, M. Neumann and B. Shader: Characteristic vertices of weighted trees via Perron values.Linear and Multilinear Algebra 40 (1996), 311–325. MR 1384650, 10.1080/03081089608818448 |
| Reference:
|
[5] R. Merris: Characteristic vertices of trees.Linear and Multilinear Algebra 22 (1987), 115–131. Zbl 0636.05021, MR 0936566, 10.1080/03081088708817827 |
| Reference:
|
[6] R. Merris: Laplacian matrices of graphs: a survey.Linear Algebra Appl. 197/198 (1994), 143–176. Zbl 0802.05053, MR 1275613 |
| . |
