| Title:
|
Some properties of the distance Laplacian eigenvalues of a graph (English) |
| Author:
|
Aouchiche, Mustapha |
| Author:
|
Hansen, Pierre |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
751-761 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The distance Laplacian of a connected graph $G$ is defined by $\mathcal {L} = {\rm Diag(Tr)}- \mathcal {D}$, where $\mathcal {D}$ is the distance matrix of $G$, and ${\rm Diag(Tr)}$ is the diagonal matrix whose main entries are the vertex transmissions in $G$. The spectrum of $\mathcal {L}$ is called the distance Laplacian spectrum of $G$. In the present paper, we investigate some particular distance Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance Laplacian eigenvalues. We establish some properties of the distance Laplacian spectrum that enable us to derive the distance Laplacian characteristic polynomials for several classes of graphs. (English) |
| Keyword:
|
distance matrix |
| Keyword:
|
Laplacian |
| Keyword:
|
characteristic polynomial |
| Keyword:
|
eigenvalue |
| MSC:
|
05C12 |
| MSC:
|
05C31 |
| MSC:
|
05C50 |
| MSC:
|
05C76 |
| idZBL:
|
Zbl 06391522 |
| idMR:
|
MR3298557 |
| DOI:
|
10.1007/s10587-014-0129-2 |
| . |
| Date available:
|
2014-12-19T16:09:08Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144055 |
| . |
| Reference:
|
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