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For a commutative ring $R,$ with non-zero zero divisors $Z^{\ast}(R)$. Thezero divisor graph $\Gamma(R)$ is a simple graph with vertex set $Z^{\ast}(R)$,and two distinct vertices $x,y\in V(\Gamma(R))$ are adjacent if and only if$x\cdot y=0.$ In this note, we provide counter examples to the eigenvalues, theenergy and the second Zagreb index related to zero divisor graphs of ringsobtained in [Johnson and Sankar, J. Appl. Math. Comp. (2023), \cite{johnson}].We correct the eigenvalues (energy) and the Zagreb index result for the zerodivisor graphs of ring $\mathbb{Z}_{p}[x]/\langle x^{4} \rangle.$ We show thatfor any prime $p$, $\Gamma(\mathbb{Z}_{p}[x]/\langle x^{4} \rangle)$ isnon-hyperenergetic and for prime $p\geq 3$, $\Gamma(\mathbb{Z}_{p}[x]/\langlex^{4} \rangle)$ is hypoenergetic. We give a formulae for the topologicalindices of $\Gamma(\mathbb{Z}_{p}[x]/\langle x^{4} \rangle)$ and show that itsZagreb indices satisfy Hansen and Vuki$\check{c}$cevi\'c conjecture\cite{hansen}.

A note on eigenvalues of zero divisor graphs associated with commutative rings