| Title:
|
Remarks on $D$-integral complete multipartite graphs (English) |
| Author:
|
Híc, Pavel |
| Author:
|
Pokorný, Milan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
457-464 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A graph is called distance integral (or $D$-integral) if all eigenvalues of its distance matrix are integers. In their study of $D$-integral complete multipartite graphs, Yang and Wang (2015) posed two questions on the existence of such graphs. We resolve these questions and present some further results on $D$-integral complete multipartite graphs. We give the first known distance integral complete multipartite graphs $K_{p_{1},p_{2},p_{3}}$ with $p_{1}<p_{2}<p_{3}$, and $K_{p_{1},p_{2},p_{3},p_{4}}$ with $p_{1}<p_{2}<p_{3}<p_{4}$, as well as the infinite classes of distance integral complete multipartite graphs $K_{a_{1} p_{1},a_{2} p_{2},\ldots ,a_{s} p_{s}}$ with $s=5,6$. (English) |
| Keyword:
|
distance spectrum |
| Keyword:
|
integral graph |
| Keyword:
|
distance integral graph |
| Keyword:
|
complete multipartite graph |
| MSC:
|
05C50 |
| idZBL:
|
Zbl 06604479 |
| idMR:
|
MR3519614 |
| DOI:
|
10.1007/s10587-016-0268-8 |
| . |
| Date available:
|
2016-06-16T12:54:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145736 |
| . |
| Reference:
|
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