| Title:
|
Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings (English) |
| Author:
|
Jalali, Mitra |
| Author:
|
Tehranian, Abolfazl |
| Author:
|
Nikandish, Reza |
| Author:
|
Rasouli, Hamid |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
27-34 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a commutative ring with identity and $A(R)$ be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of $R$ is defined as the graph ${\rm SAG}(R)$ with the vertex set $A(R)^*=A(R)\setminus\{0\}$ and two distinct vertices $I$ and $J$ are adjacent if and only if $I\cap {\rm Ann}(J)\neq (0)$ and $J\cap {\rm Ann}(I)\neq (0)$. In this paper, the perfectness of ${\rm SAG}(R)$ for some classes of rings $R$ is investigated. (English) |
| Keyword:
|
strongly annihilating-ideal graph |
| Keyword:
|
perfect graph |
| Keyword:
|
chromatic number |
| Keyword:
|
clique number |
| MSC:
|
05C25 |
| MSC:
|
05C99 |
| MSC:
|
13A15 |
| MSC:
|
13B99 |
| idZBL:
|
Zbl 07217156 |
| idMR:
|
MR4093427 |
| DOI:
|
10.14712/1213-7243.2020.005 |
| . |
| Date available:
|
2020-04-30T11:13:58Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148073 |
| . |
| Reference:
|
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| . |
