Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 2 2026 04 01 LAPLACIAN SPECTRUM AND ENERGY OF NON-COMMUTING GRAPHS OF FINITE RINGS 209 244 3733 10.22044/jas.2024.14111.1802 EN Monalisha Sharma Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India. Department of Mathematics, Baosi Banikanta Kakati College Nagaon, Barpeta, PIN - 781311, Assam, India. Rajat Kanti Nath Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India. Journal Article 2024 01 26 We compute spectrum, energy, Laplacian spectrum/ energy and signless Laplacian spectrum/energy of non-commuting graphs of certain finite non-commutative rings. In particular, we consider finite rings $R$ such that $|R| = p^2, p^3, p^4$, $p^5$, $p^2q$ and $p^3q$, where $p$ and $q$ are primes. Further, we consider $n$-centralizer finite\\ rings for $n \, = \,4, \, 5$ \, and \, $p \,+ \,2$; \, more generally, finite rings with central quotients isomorphic to $\mathbb{Z}_p \times \mathbb{Z}_p$. Our computations reveal that non-commuting graphs of these rings are L-integral. We also determine whether non-commuting graphs of these rings are integral, Q-integral, hyperenergetic, L-hyperenergetic or Q-hyperenergetic. https://jas.shahroodut.ac.ir/article_3733_a0fa3cd589474451f4ae7f8a796ebaa3.pdf