| Title:
|
A co-ideal based identity-summand graph of a commutative semiring (English) |
| Author:
|
Atani, S. Ebrahimi |
| Author:
|
Hesari, S. Dolati Pish |
| Author:
|
Khoramdel, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
269-285 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $I$ be a strong co-ideal of a commutative semiring $R$ with identity. Let $\Gamma_{I} (R)$ be a graph with the set of vertices $S_{I} (R) = \{x \in R\setminus I: x + y \in I$ for some $y \in R \setminus I\}$, where two distinct vertices $x$ and $y$ are adjacent if and only if $x + y \in I$. We look at the diameter and girth of this graph. Also we discuss when $\Gamma_{I} (R)$ is bipartite. Moreover, studies are done on the planarity, clique, and chromatic number of this graph. Examples illustrating the results are presented. (English) |
| Keyword:
|
strong co-ideal |
| Keyword:
|
$Q$-strong co-ideal |
| Keyword:
|
identity-summand element |
| Keyword:
|
identity-summand graph |
| Keyword:
|
co-ideal based |
| MSC:
|
05C62 |
| MSC:
|
16Y60 |
| idZBL:
|
Zbl 06486993 |
| idMR:
|
MR3390276 |
| DOI:
|
10.14712/1213-7243.2015.124 |
| . |
| Date available:
|
2015-07-09T20:40:24Z |
| Last updated:
|
2017-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144344 |
| . |
| Reference:
|
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