on cozero divisor graphs of ring $z_n$

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 $xnotin ry$ and $ynotin rx$, where $xr$ is the ideal generated by $x$. in this article we find the spectra of $gamma^{prime}(mathbb{z}_{n}) $ for $nin {q_{1}q_{2}, q_{1}q_{2}q_{3},q_{1}^{n_{1}}q_{2}},$ 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.