Classes of graphs that are not Cohen–Macaulay classes
UDC 512.5 Characterizations of the classes of Cohen–Macaulay graphs are important because when we characterize one of these classes, then we can decide whether a ring of the form $\mathbb{K}[x_1,\ldots,x_n]/I$ is Cohen–Macaulay or not, where $I$ is a square-free monomial ideal. For a given commutat...
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| Date: | 2025 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8093 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512892041822208 |
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| author | Asir, T. Ashitha, T. Asir, T. Ashitha, T. |
| author_facet | Asir, T. Ashitha, T. Asir, T. Ashitha, T. |
| author_sort | Asir, T. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-11-05T09:34:36Z |
| description | UDC 512.5
Characterizations of the classes of Cohen–Macaulay graphs are important because when we characterize one of these classes, then we can decide whether a ring of the form $\mathbb{K}[x_1,\ldots,x_n]/I$ is Cohen–Macaulay or not, where $I$ is a square-free monomial ideal. For a given commutative ring $R$, the total graph of $R$ is a simple graph with $R$ as the vertex set and two distinct vertices $x$ and $y$ are adjacent if $x+y$ is a zero-divisor of $R$. We find two classes of the total graphs that are not Cohen–Macaulay classes. |
| doi_str_mv | 10.3842/umzh.v77i2.8093 |
| first_indexed | 2026-03-24T03:36:00Z |
| format | Article |
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| id | umjimathkievua-article-8093 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:36:00Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-80932025-11-05T09:34:36Z Classes of graphs that are not Cohen–Macaulay classes Classes of graphs that are not Cohen–Macaulay classes Asir, T. Ashitha, T. Asir, T. Ashitha, T. Well-covered graph Cohen--Macaulay graph Total graph of a ring Mathematics UDC 512.5 Characterizations of the classes of Cohen–Macaulay graphs are important because when we characterize one of these classes, then we can decide whether a ring of the form $\mathbb{K}[x_1,\ldots,x_n]/I$ is Cohen–Macaulay or not, where $I$ is a square-free monomial ideal. For a given commutative ring $R$, the total graph of $R$ is a simple graph with $R$ as the vertex set and two distinct vertices $x$ and $y$ are adjacent if $x+y$ is a zero-divisor of $R$. We find two classes of the total graphs that are not Cohen–Macaulay classes. УДК 512.5 Класи графів, що не є класами Коена–Маколея Характеризація класів графів Коена–Маколея є важливою, тому що у випадку, коли ми характеризуємо один із цих класів, дійсно можна стверджувати, чи є кільце форми $\mathbb{K}[x_1,\ldots,x_n]/I,$ де $I$ – безквадратний мономіальний ідеал, кільцем Коена–Маколея, чи ні. Загальний граф для цього комутативного кільця $R$ є простим графом, в якому $R$ – набір вершин, а дві різні вершини $x$ і $y$ суміжні, якщо $x+y$ – дільник нуля $R$. Наведено два класи тотальних графів, які не є класами Коена–Маколея. Institute of Mathematics, NAS of Ukraine 2025-11-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8093 10.3842/umzh.v77i2.8093 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 2 (2025); 153–154 Український математичний журнал; Том 77 № 2 (2025); 153–154 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8093/10344 Copyright (c) 2025 T. Asir, T. Ashitha |
| spellingShingle | Asir, T. Ashitha, T. Asir, T. Ashitha, T. Classes of graphs that are not Cohen–Macaulay classes |
| title | Classes of graphs that are not Cohen–Macaulay classes |
| title_alt | Classes of graphs that are not Cohen–Macaulay classes |
| title_full | Classes of graphs that are not Cohen–Macaulay classes |
| title_fullStr | Classes of graphs that are not Cohen–Macaulay classes |
| title_full_unstemmed | Classes of graphs that are not Cohen–Macaulay classes |
| title_short | Classes of graphs that are not Cohen–Macaulay classes |
| title_sort | classes of graphs that are not cohen–macaulay classes |
| topic_facet | Well-covered graph Cohen--Macaulay graph Total graph of a ring Mathematics |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8093 |
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