Laplacian spectrum of the unit graph associated to the ring of integers modulo pq
Let $ R $ be a ring and $ U(R) $ be the set of unit elements of $ R $. The unit graph $ G(R) $ of $ R $ is the graph whose vertices are all the elements of $ R $, defining distinct vertices $ x $ and $ y $ to be adjacent if and only if $ x + y \in U(R) $. The Laplacian spectrum of $ G(\mathbb{Z}_n)...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024200?viewType=HTML |
| _version_ | 1827358049412579328 |
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| author | Wafaa Fakieh Amal Alsaluli Hanaa Alashwali |
| author_facet | Wafaa Fakieh Amal Alsaluli Hanaa Alashwali |
| author_sort | Wafaa Fakieh |
| collection | DOAJ |
| description | Let $ R $ be a ring and $ U(R) $ be the set of unit elements of $ R $. The unit graph $ G(R) $ of $ R $ is the graph whose vertices are all the elements of $ R $, defining distinct vertices $ x $ and $ y $ to be adjacent if and only if $ x + y \in U(R) $. The Laplacian spectrum of $ G(\mathbb{Z}_n) $ was studied when $ n = p^{m} $, where $ p $ is a prime and $ m $ is a positive integer. Consequently, in this paper, we study the Laplacian spectrum of $ G(\mathbb{Z}_n) $, for $ n = p_1p_2...p_k $, where $ p_i $ are distinct primes and $ i = 1, 2, ..., k $. |
| first_indexed | 2024-03-08T05:57:09Z |
| format | Article |
| id | doaj.art-e8c59be3628947f8ac3a57f5d09b4e8c |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:57:09Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-e8c59be3628947f8ac3a57f5d09b4e8c2024-02-05T01:24:49ZengAIMS PressAIMS Mathematics2473-69882024-01-01924098410810.3934/math.2024200Laplacian spectrum of the unit graph associated to the ring of integers modulo pqWafaa Fakieh0Amal Alsaluli 1Hanaa Alashwali21. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia1. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia 2. Department of Mathematics, Faculty of Science, University of Bisha, Bisha 61922, Saudi Arabia1. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaLet $ R $ be a ring and $ U(R) $ be the set of unit elements of $ R $. The unit graph $ G(R) $ of $ R $ is the graph whose vertices are all the elements of $ R $, defining distinct vertices $ x $ and $ y $ to be adjacent if and only if $ x + y \in U(R) $. The Laplacian spectrum of $ G(\mathbb{Z}_n) $ was studied when $ n = p^{m} $, where $ p $ is a prime and $ m $ is a positive integer. Consequently, in this paper, we study the Laplacian spectrum of $ G(\mathbb{Z}_n) $, for $ n = p_1p_2...p_k $, where $ p_i $ are distinct primes and $ i = 1, 2, ..., k $.https://www.aimspress.com/article/doi/10.3934/math.2024200?viewType=HTMLunit graphlaplacian matrixlaplacian spectrumdirect productring of integers modulo n |
| spellingShingle | Wafaa Fakieh Amal Alsaluli Hanaa Alashwali Laplacian spectrum of the unit graph associated to the ring of integers modulo pq AIMS Mathematics unit graph laplacian matrix laplacian spectrum direct product ring of integers modulo n |
| title | Laplacian spectrum of the unit graph associated to the ring of integers modulo pq |
| title_full | Laplacian spectrum of the unit graph associated to the ring of integers modulo pq |
| title_fullStr | Laplacian spectrum of the unit graph associated to the ring of integers modulo pq |
| title_full_unstemmed | Laplacian spectrum of the unit graph associated to the ring of integers modulo pq |
| title_short | Laplacian spectrum of the unit graph associated to the ring of integers modulo pq |
| title_sort | laplacian spectrum of the unit graph associated to the ring of integers modulo pq |
| topic | unit graph laplacian matrix laplacian spectrum direct product ring of integers modulo n |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024200?viewType=HTML |
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