| Title:
|
A note on another construction of graphs with $4n+6$ vertices and cyclic automorphism group of order $4n$ (English) |
| Author:
|
Daugulis, Peteris |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
13-18 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having $4n+6$ vertices and automorphism group cyclic of order $4n$, $n\ge 1$. As a special case we get graphs with $2^k+6$ vertices and cyclic automorphism groups of order $2^k$. It can revive interest in related problems. (English) |
| Keyword:
|
graph |
| Keyword:
|
automorphism group |
| MSC:
|
05C25 |
| MSC:
|
05C35 |
| MSC:
|
05C75 |
| MSC:
|
05E18 |
| idZBL:
|
Zbl 06738495 |
| idMR:
|
MR3636678 |
| DOI:
|
10.5817/AM2017-1-13 |
| . |
| Date available:
|
2017-03-23T10:01:55Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146072 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Babai, L.: In Graham R.L.; Grotschel M.; Lovasz L., Handbook of Combinatorics I.n Graham R.L.; Grotschel M.; Lovasz L., Handbook of Combinatorics I, ch. Automorphism groups, isomorphism, reconstruction, pp. 1447–1540, North-Holland, 1995. MR 1373683 |
| Reference:
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| Reference:
|
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| Reference:
|
[6] Daugulis, P.: $10$-vertex graphs with cyclic automorphism group of order $4$.2014, http://arxiv.org/abs/1410.1163. |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| . |
