Nonessential sum graph of an Artinian ring
Purpose – The authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”. The nonessential sum graph, denoted by NES(R), of a commutative ring R with unity is an undirected graph whose vertex set is the collection of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Emerald Publishing
2022-01-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2020-0039/full/pdf |
| _version_ | 1797791684804739072 |
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| author | Bikash Barman Kukil Kalpa Rajkhowa |
| author_facet | Bikash Barman Kukil Kalpa Rajkhowa |
| author_sort | Bikash Barman |
| collection | DOAJ |
| description | Purpose – The authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”. The nonessential sum graph, denoted by NES(R), of a commutative ring R with unity is an undirected graph whose vertex set is the collection of all nonessential ideals of R and any two vertices are adjacent if and only if their sum is also a nonessential ideal of R. Design/methodology/approach – The method is theoretical. Findings – The authors obtain some properties of NES(R) related with connectedness, diameter, girth, completeness, cut vertex, r-partition and regular character. The clique number, independence number and domination number of NES(R) are also found. Originality/value – The paper is original. |
| first_indexed | 2024-03-13T02:22:21Z |
| format | Article |
| id | doaj.art-c3549dd6c7ee4e3b94920dec55f0d1bb |
| institution | Directory Open Access Journal |
| issn | 1319-5166 2588-9214 |
| language | English |
| last_indexed | 2024-03-13T02:22:21Z |
| publishDate | 2022-01-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-c3549dd6c7ee4e3b94920dec55f0d1bb2023-06-30T09:18:54ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142022-01-01281374310.1108/AJMS-08-2020-0039Nonessential sum graph of an Artinian ringBikash Barman0Kukil Kalpa Rajkhowa1Cotton University, Guwahati, IndiaCotton University, Guwahati, IndiaPurpose – The authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”. The nonessential sum graph, denoted by NES(R), of a commutative ring R with unity is an undirected graph whose vertex set is the collection of all nonessential ideals of R and any two vertices are adjacent if and only if their sum is also a nonessential ideal of R. Design/methodology/approach – The method is theoretical. Findings – The authors obtain some properties of NES(R) related with connectedness, diameter, girth, completeness, cut vertex, r-partition and regular character. The clique number, independence number and domination number of NES(R) are also found. Originality/value – The paper is original.https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2020-0039/full/pdfNonessential idealNonessential sum graphMinimal ideal |
| spellingShingle | Bikash Barman Kukil Kalpa Rajkhowa Nonessential sum graph of an Artinian ring Arab Journal of Mathematical Sciences Nonessential ideal Nonessential sum graph Minimal ideal |
| title | Nonessential sum graph of an Artinian ring |
| title_full | Nonessential sum graph of an Artinian ring |
| title_fullStr | Nonessential sum graph of an Artinian ring |
| title_full_unstemmed | Nonessential sum graph of an Artinian ring |
| title_short | Nonessential sum graph of an Artinian ring |
| title_sort | nonessential sum graph of an artinian ring |
| topic | Nonessential ideal Nonessential sum graph Minimal ideal |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2020-0039/full/pdf |
| work_keys_str_mv | AT bikashbarman nonessentialsumgraphofanartinianring AT kukilkalparajkhowa nonessentialsumgraphofanartinianring |