| Title:
|
Graphs with small diameter determined by their $D$-spectra (English) |
| Author:
|
Liu, Ruifang |
| Author:
|
Xue, Jie |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
1-17 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a connected graph with vertex set $V(G)=\{v_{1},v_{2},\ldots ,v_{n}\}$. The distance matrix $D(G)=(d_{ij})_{n\times n}$ is the matrix indexed by the vertices of\/ $G$, where $d_{ij}$ denotes the distance between the vertices $v_{i}$ and $v_{j}$. Suppose that $\lambda _{1}(D)\geq \lambda _{2}(D)\geq \nobreak \cdots \geq \lambda _{n}(D)$ are the distance spectrum of $G$. The graph $G$ is said to be determined by its \hbox {$D$-spectrum} if with respect to the distance matrix $D(G)$, any graph having the same spectrum as $G$ is isomorphic to $G$. We give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined by their $D$-spectra. (English) |
| Keyword:
|
distance spectrum |
| Keyword:
|
distance characteristic polynomial |
| Keyword:
|
$D$-spectrum determined by its $D$-spectrum |
| MSC:
|
05C50 |
| idZBL:
|
Zbl 06861564 |
| idMR:
|
MR3783582 |
| DOI:
|
10.21136/CMJ.2018.0505-15 |
| . |
| Date available:
|
2018-03-19T10:23:40Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147116 |
| . |
| Reference:
|
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