| Title:
|
On iteration digraph and zero-divisor graph of the ring $\mathbb {Z}_n$ (English) |
| Author:
|
Ju, Tengxia |
| Author:
|
Wu, Meiyun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
611-628 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the first part, we assign to each positive integer $n$ a digraph $\Gamma (n,5),$ whose set of vertices consists of elements of the ring $\mathbb {Z}_n=\{0,1,\cdots ,n-1\}$ with the addition and the multiplication operations modulo $n,$ and for which there is a directed edge from $a$ to $b$ if and only if $a^5\equiv b\pmod n$. Associated with $\Gamma (n,5)$ are two disjoint subdigraphs: $\Gamma _1(n,5)$ and $\Gamma _2(n,5)$ whose union is $\Gamma (n,5).$ The vertices of $\Gamma _1(n,5)$ are coprime to $n,$ and the vertices of $\Gamma _2(n,5)$ are not coprime to $n.$ In this part, we study the structure of $\Gamma (n,5)$ in detail. \endgraf In the second part, we investigate the zero-divisor graph $G(\mathbb {Z}_n)$ of the ring $\mathbb {Z}_n.$ Its vertex- and edge-connectivity are discussed. (English) |
| Keyword:
|
iteration digraph |
| Keyword:
|
zero-divisor graph |
| Keyword:
|
tree |
| Keyword:
|
cycle |
| Keyword:
|
vertex-connectivity |
| MSC:
|
05C20 |
| MSC:
|
05C25 |
| MSC:
|
11A07 |
| idZBL:
|
Zbl 06391515 |
| idMR:
|
MR3298550 |
| DOI:
|
10.1007/s10587-014-0122-9 |
| . |
| Date available:
|
2014-12-19T15:56:19Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144048 |
| . |
| Reference:
|
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| Reference:
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| . |
