Component graphs of vector spaces and zero-divisor graphs of ordered sets
In this paper, nonzero component graphs and nonzero component union graphs of finite-dimensional vector spaces are studied using the zero-divisor graph of a specially constructed 0–1-distributive lattice and the zero-divisor graph of rings. Furthermore, we define an equivalence relation on nonzero c...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-05-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2025.2449683 |
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| author | Nilesh Khandekar Peter J. Cameron Vinayak Joshi |
| author_facet | Nilesh Khandekar Peter J. Cameron Vinayak Joshi |
| author_sort | Nilesh Khandekar |
| collection | DOAJ |
| description | In this paper, nonzero component graphs and nonzero component union graphs of finite-dimensional vector spaces are studied using the zero-divisor graph of a specially constructed 0–1-distributive lattice and the zero-divisor graph of rings. Furthermore, we define an equivalence relation on nonzero component graphs and nonzero component union graphs to deduce that these graphs are the graph join of zero-divisor graphs of Boolean algebras and complete graphs. The last section characterizes the perfect and chordal nonzero component and nonzero component union graphs. Additionally, we observe that the nonzero component graph and reduced nonzero component union graph of free semi-modules could be treated as the zero-divisor graph of a 0–1-distributive lattice. |
| format | Article |
| id | doaj-art-be333338bfb24d4fb966dff54cfab41b |
| institution | Kabale University |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj-art-be333338bfb24d4fb966dff54cfab41b2025-08-20T06:46:14ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742025-05-0122220421010.1080/09728600.2025.2449683Component graphs of vector spaces and zero-divisor graphs of ordered setsNilesh Khandekar0Peter J. Cameron1Vinayak Joshi2Department of Mathematics, Savitribai Phule Pune University, Pune, Maharashtra, IndiaSchool of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, UKDepartment of Mathematics, Savitribai Phule Pune University, Pune, Maharashtra, IndiaIn this paper, nonzero component graphs and nonzero component union graphs of finite-dimensional vector spaces are studied using the zero-divisor graph of a specially constructed 0–1-distributive lattice and the zero-divisor graph of rings. Furthermore, we define an equivalence relation on nonzero component graphs and nonzero component union graphs to deduce that these graphs are the graph join of zero-divisor graphs of Boolean algebras and complete graphs. The last section characterizes the perfect and chordal nonzero component and nonzero component union graphs. Additionally, we observe that the nonzero component graph and reduced nonzero component union graph of free semi-modules could be treated as the zero-divisor graph of a 0–1-distributive lattice.https://www.tandfonline.com/doi/10.1080/09728600.2025.2449683Nonzero component graphnonzero component union graphzero-divisor graphperfect graphchordal graph15A03 |
| spellingShingle | Nilesh Khandekar Peter J. Cameron Vinayak Joshi Component graphs of vector spaces and zero-divisor graphs of ordered sets AKCE International Journal of Graphs and Combinatorics Nonzero component graph nonzero component union graph zero-divisor graph perfect graph chordal graph 15A03 |
| title | Component graphs of vector spaces and zero-divisor graphs of ordered sets |
| title_full | Component graphs of vector spaces and zero-divisor graphs of ordered sets |
| title_fullStr | Component graphs of vector spaces and zero-divisor graphs of ordered sets |
| title_full_unstemmed | Component graphs of vector spaces and zero-divisor graphs of ordered sets |
| title_short | Component graphs of vector spaces and zero-divisor graphs of ordered sets |
| title_sort | component graphs of vector spaces and zero divisor graphs of ordered sets |
| topic | Nonzero component graph nonzero component union graph zero-divisor graph perfect graph chordal graph 15A03 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2025.2449683 |
| work_keys_str_mv | AT nileshkhandekar componentgraphsofvectorspacesandzerodivisorgraphsoforderedsets AT peterjcameron componentgraphsofvectorspacesandzerodivisorgraphsoforderedsets AT vinayakjoshi componentgraphsofvectorspacesandzerodivisorgraphsoforderedsets |