For a commutative ring R, with non-zero zero divisors \(Z^{*}(R)\) . The zero divisor graph \(\Gamma (R)\) is a simple graph with vertex set \(Z^{*}(R)\) , and two distinct vertices \(x,y\in V(\Gamma (R))\) are adjacent if and only if \(x\cdot y=0.\) This article presents counter examples for the energy, the second Zagreb index, and the eigenvalues associated with zero divisor graphs of rings that were found in [Johnson and Sankar, J. Appl. Math. Comp. (2023)]. For the zero divisor graph \(\mathbb {Z}_{p}[x]/\langle x^{4} \rangle \) , we rectify the eigenvalues (energy) and the Zagreb index results. We show that for any prime p, \(\Gamma (\mathbb {Z}_{p}[x]/\langle x^{4} \rangle )\) is non-hyperenergetic and for prime \(p\ge 3\) , \(\Gamma (\mathbb {Z}_{p}[x]/\langle x^{4} \rangle )\) is hypoenergetic. We give a formulae for the topological indices of \(\Gamma (\mathbb {Z}_{p}[x]/\langle x^{4} \rangle )\) and show that its Zagreb indices satisfy Zagreb Conjecture [Hansen and Vukičcević, Croatica Chem. Acta, (2007)].
