On iteration digraph and zero-divisor graph of the ring $\mathbb {Z}_n$

Title:

On iteration digraph and zero-divisor graph of the ring $\mathbb {Z}_n$

Creator:

Ju, Tengxia and Wu, Metyun

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:308b7d8c-8a83-490c-b542-0c94e598c820
uuid:308b7d8c-8a83-490c-b542-0c94e598c820

Subject:

iteration digraph, zero-divisor graph, tree, cycle, and vertex-connectivity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

611-628

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:3

Harvested from:

CDK

Metadata only:

false