| Title:
|
Resolving sets of directed Cayley graphs for the direct product of cyclic groups (English) |
| Author:
|
Mengesha, Demelash Ashagrie |
| Author:
|
Vetrík, Tomáš |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
621-636 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A directed Cayley graph $C(\Gamma ,X)$ is specified by a group $\Gamma $ and an identity-free generating set $X$ for this group. Vertices of $C(\Gamma ,X)$ are elements of $\Gamma $ and there is a directed edge from the vertex $u$ to the vertex $v$ in $C(\Gamma ,X)$ if and only if there is a generator $x \in X$ such that $ux = v$. We study graphs $C(\Gamma ,X)$ for the direct product $Z_m \times Z_n$ of two cyclic groups $Z_m$ and $Z_n$, and the generating set $X = \{ (0,1), (1, 0), (2,0), \dots , (p,0) \}$. We present resolving sets which yield upper bounds on the metric dimension of these graphs for $p = 2$ and $3$. (English) |
| Keyword:
|
metric dimension |
| Keyword:
|
resolving set |
| Keyword:
|
Cayley graph |
| Keyword:
|
direct product |
| Keyword:
|
cyclic group |
| MSC:
|
05C12 |
| MSC:
|
05C25 |
| idZBL:
|
Zbl 07088808 |
| idMR:
|
MR3989270 |
| DOI:
|
10.21136/CMJ.2019.0127-17 |
| . |
| Date available:
|
2019-07-24T11:15:08Z |
| Last updated:
|
2021-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147781 |
| . |
| Reference:
|
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| Reference:
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