Exploring the structure and properties of ideal-based zero-divisor graphs in involution near rings
For an involution near ring 𝒩 and its ideal ℐ, the text introduces an involution ideal-based zero- divisor graph Γℐ*(𝒩) which is an undirected graph with vertex set { x ∈ 𝒩 - ℐ: x𝒩y ⊂ ℐ (or y𝒩x ⊂ ℑ ) for some y ∈ 𝒩-ℐ}, where two distinct vertices x and y are adjacent if and only if y𝒩x* ⊂...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2024-03-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | https://www.utgjiu.ro/math/sma/v19/p19_06.pdf |
| _version_ | 1797255682698772480 |
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| author | Masreshaw Walle Abate Wang Yao |
| author_facet | Masreshaw Walle Abate Wang Yao |
| author_sort | Masreshaw Walle Abate |
| collection | DOAJ |
| description | For an involution near ring 𝒩 and its ideal ℐ, the text introduces an involution ideal-based zero- divisor graph Γℐ*(𝒩) which is an undirected graph with vertex set
{ x ∈ 𝒩 - ℐ: x𝒩y ⊂ ℐ (or y𝒩x ⊂ ℑ ) for some y ∈ 𝒩-ℐ},
where two distinct vertices x and y are adjacent if and only if y𝒩x* ⊂ ℐ or x𝒩y* ⊂ ℐ. The paper provides characterizations of Γℐ*(𝒩) when it forms a complete graph or a star graph. It also explores the structure of Γℐ*(𝒩), investigates its properties like connectedness with diam(Γℐ*(𝒩)) ≤ 3 and analyzes the connection of Γℐ*(𝒩) with Γℐ*(𝒩/ℐ). Furthermore, the paper discusses the chromatic number and clique number of the graph. It also characterizes all right permutable *-near-rings 𝒩 for which the graph Γℐ*(𝒩) can be with a finite chromatic number. |
| first_indexed | 2024-04-24T22:09:44Z |
| format | Article |
| id | doaj.art-c4a4abb3c218445e9f7fb1b1b158e38c |
| institution | Directory Open Access Journal |
| issn | 1843-7265 1842-6298 |
| language | English |
| last_indexed | 2024-04-24T22:09:44Z |
| publishDate | 2024-03-01 |
| publisher | University Constantin Brancusi of Targu-Jiu |
| record_format | Article |
| series | Surveys in Mathematics and its Applications |
| spelling | doaj.art-c4a4abb3c218445e9f7fb1b1b158e38c2024-03-20T10:13:55ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982024-03-0119 (2024)109126Exploring the structure and properties of ideal-based zero-divisor graphs in involution near ringsMasreshaw Walle Abate0Wang Yao1School of Mathematics and Statistics, Nanjing University of Information Science and Technology, 219 Ningliu Road, Nanjing 210044, China. and Department of Mathematics, Dilla University, 419 Dilla, EthiopiaSchool of Mathematics and Statistics, Nanjing University of Information Science and Technology, 219 Ningliu Road, Nanjing 210044, China.For an involution near ring 𝒩 and its ideal ℐ, the text introduces an involution ideal-based zero- divisor graph Γℐ*(𝒩) which is an undirected graph with vertex set { x ∈ 𝒩 - ℐ: x𝒩y ⊂ ℐ (or y𝒩x ⊂ ℑ ) for some y ∈ 𝒩-ℐ}, where two distinct vertices x and y are adjacent if and only if y𝒩x* ⊂ ℐ or x𝒩y* ⊂ ℐ. The paper provides characterizations of Γℐ*(𝒩) when it forms a complete graph or a star graph. It also explores the structure of Γℐ*(𝒩), investigates its properties like connectedness with diam(Γℐ*(𝒩)) ≤ 3 and analyzes the connection of Γℐ*(𝒩) with Γℐ*(𝒩/ℐ). Furthermore, the paper discusses the chromatic number and clique number of the graph. It also characterizes all right permutable *-near-rings 𝒩 for which the graph Γℐ*(𝒩) can be with a finite chromatic number. https://www.utgjiu.ro/math/sma/v19/p19_06.pdfnear ringzero-divisor-graphideal based zero-divisor graphideal of *-near-ringgraph coloringchromatic number |
| spellingShingle | Masreshaw Walle Abate Wang Yao Exploring the structure and properties of ideal-based zero-divisor graphs in involution near rings Surveys in Mathematics and its Applications near ring zero-divisor-graph ideal based zero-divisor graph ideal of *-near-ring graph coloring chromatic number |
| title | Exploring the structure and properties of ideal-based zero-divisor graphs in involution near rings |
| title_full | Exploring the structure and properties of ideal-based zero-divisor graphs in involution near rings |
| title_fullStr | Exploring the structure and properties of ideal-based zero-divisor graphs in involution near rings |
| title_full_unstemmed | Exploring the structure and properties of ideal-based zero-divisor graphs in involution near rings |
| title_short | Exploring the structure and properties of ideal-based zero-divisor graphs in involution near rings |
| title_sort | exploring the structure and properties of ideal based zero divisor graphs in involution near rings |
| topic | near ring zero-divisor-graph ideal based zero-divisor graph ideal of *-near-ring graph coloring chromatic number |
| url | https://www.utgjiu.ro/math/sma/v19/p19_06.pdf |
| work_keys_str_mv | AT masreshawwalleabate exploringthestructureandpropertiesofidealbasedzerodivisorgraphsininvolutionnearrings AT wangyao exploringthestructureandpropertiesofidealbasedzerodivisorgraphsininvolutionnearrings |