| Title:
|
Coloring of graph of ring with respect to idempotents (English) |
| Author:
|
Patil, Avinash |
| Author:
|
Patil, Dipika |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
150 |
| Issue:
|
4 |
| Year:
|
2025 |
| Pages:
|
573-582 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a ring with nonzero identity. A graph $G_{{\rm Id}}(R)$ of $R$ with respect to idempotents of $R$ has elements of $R$ as vertices and distinct vertices $x$, $y$ are adjacent if and only if $x + y$ is an idempotent of $R$. In this paper, we prove that $G_{{\rm Id}}(R)$ is weakly perfect and provide a condition for the perfectness of the same. Further, we characterize finite abelian rings for which the complement of $G_{{\rm Id}}(R)$ is connected. (English) |
| Keyword:
|
idempotent graph |
| Keyword:
|
weak perfect graph |
| Keyword:
|
zero-divisor graph |
| MSC:
|
05C15 |
| MSC:
|
05C17 |
| MSC:
|
05C25 |
| DOI:
|
10.21136/MB.2025.0024-24 |
| . |
| Date available:
|
2025-11-07T19:26:52Z |
| Last updated:
|
2025-11-16 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153163 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| . |
