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On cozero divisor graphs of ring $Z_n$ | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 تیر 1403 اصل مقاله (473.08 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.26112.1974 | ||
| نویسندگان | ||
| Zahid Raza1؛ Bilal Ahmad Rather2؛ Modjtaba Ghorbani* 3 | ||
| 1Department of Mathematics, College of Sciences, University of Sharjah, UAE | ||
| 2Mathematical Sciences Department, College of Science, United Arab Emirates University, Al Ain 15551, Abu Dhabi, UAE | ||
| 3Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, I.R. Iran | ||
| چکیده | ||
| The cozero divisor graph $\Gamma^{\prime}(R)$ of a commutative ring $R$ is a simple graph with vertex set as non-zero zero divisor elements of $R$ such that two distinct vertices $x$ and $y$ are adjacent iff $x\notin Ry$ and $y\notin Rx$, where $xR$ is the ideal generated by $x$. In this article we find the spectra of $\Gamma^{\prime}(\mathbb{Z}_{n}) $ for $n\in \{q_{1}q_{2}, q_{1}q_{2}q_{3},q_{1}^{n_{1}}q_{2}\},$ where $q_{i}$'s are primes. As a consequence we obtain the bounds for the largest (smallest) eigenvalues, bounds for spread, rank and inertia of $ \Gamma^{\prime}(\mathbb{Z}_{q_{1}^{n_{1}}q_{2}})$ along with the determinant, inverse and square of trace of its quotient matrix. We present the extremal bounds for the energy of $\Gamma^{\prime}(\mathbb{Z}_{n})$ for $n=q_{1}^{n_{1}}q_{2}$ and characterize the extremal graphs attaining them. We close article with conclusion for furtherance. | ||
| کلیدواژه‌ها | ||
| Spectra؛ energy؛ Cozero divisor graphs؛ commutative rings | ||
| مراجع | ||
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