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)...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024200?viewType=HTML |
| Summary: | 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 $. |
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| ISSN: | 2473-6988 |