For a commutative ring $R,$ with non-zero zero divisors $Z^{\ast}(R)$. The zero 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, the energy and the second Zagreb index related to zero divisor graphs of rings obtained in [Johnson and Sankar, J. Appl. Math. Comp. (2023), \cite{johnson}]. We correct the eigenvalues (energy) and the Zagreb index result for the zero divisor graphs of ring $\mathbb{Z}_{p}[x]/\langle x^{4} \rangle.$ We show that for any prime $p$, $\Gamma(\mathbb{Z}_{p}[x]/\langle x^{4} \rangle)$ is non-hyperenergetic and for prime $p\geq 3$, $\Gamma(\mathbb{Z}_{p}[x]/\langle x^{4} \rangle)$ 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 Hansen and Vuki$\check{c}$cevi\'c conjecture \cite{hansen}.

翻译：对于交换环$R$，设非零零因子集合为$Z^{\ast}(R)$。零点因子图$\Gamma(R)$是以$Z^{\ast}(R)$为顶点集的简单图，两个不同顶点$x,y\in V(\Gamma(R))$相邻当且仅当$x\cdot y=0$。本文针对Johnson与Sankar在[J. Appl. Math. Comp. (2023)，\cite{johnson}]中给出的环的零点因子图特征值、能量及第二Zagreb指数提供了反例。我们修正了环$\mathbb{Z}_{p}[x]/\langle x^{4} \rangle$的零点因子图的特征值（能量）与Zagreb指数结果。证明了对任意素数$p$，$\Gamma(\mathbb{Z}_{p}[x]/\langle x^{4} \rangle)$为非超能量图，且当素数$p\geq 3$时，$\Gamma(\mathbb{Z}_{p}[x]/\langle x^{4} \rangle)$为亚能量图。我们给出了$\Gamma(\mathbb{Z}_{p}[x]/\langle x^{4} \rangle)$拓扑指数的计算公式，并证明了其Zagreb指数满足Hansen与Vuki$\check{c}$cevi\'c猜想\cite{hansen}。