| Autor: |
Bilal A. Rather, M. Aijaz, Fawad Ali, Nabil Mlaiki, Asad Ullah |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 7, Iss 7, Pp 12635-12649 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2022699?viewType=HTML |
| Popis: |
For a simple connected graph $ G $ of order $ n $, the distance signless Laplacian matrix is defined by $ D^{Q}(G) = D(G) + Tr(G) $, where $ D(G) $ and $ Tr(G) $ is the distance matrix and the diagonal matrix of vertex transmission degrees, respectively. The zero divisor graph $ \Gamma(R) $ of a finite commutative ring $ R $ is a simple graph, whose vertex set is the set of non-zero zero divisors of $ R $ and two vertices $ v, w \in \Gamma(R) $ are edge connected whenever $ vw = wv = 0 $. In this article, we find the $ D^{Q} $-eigenvalues of zero divisor graph of the ring $ \mathbb{Z}_{n} $ for general value $ n = {p_{1}^{l_{1}}p_{2}^{l_{2}}} $, where $ p_1 < p_2 $ are distinct prime numbers and $ l_{1}, l_{2} \in \mathbb{N} $. Further, we investigate the $ D^{Q} $-eigenvalues of zero divisor graphs of local rings and the rings whose associated zero divisor graphs are Hamiltonian. Also, we obtain the trace norm and the Wiener index of $ \Gamma(\mathbb{Z}_{n}) $ for some special values of $ n $. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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