Background: Chemical graph theory is a sub-branch of mathematical chemistry, assuming each atom of a molecule is a vertex and each bond between atoms as an edge. Objective: Owing to this theory, it is possible to avoid the difficulties of chemical analysis because many of the chemical properties of molecules can be determined and analyzed via topological indices. Due to these parameters, it is possible to determine the physicochemical properties, biological activities, environmental behaviours and spectral properties of molecules. Nowadays, studies on the zero divisor graph of Zn via topological indices is a trending field in spectral graph theory. Methods: For a commutative ring R with identity, the prime ideal sum graph of R is a graph whose vertices are nonzero proper ideals of R and two distinctvertices I and J are adjacent if and only if I+J is a prime ideal of R. Results: In this study the forgotten topological index and Wiener index of the prime ideal sum graph of Zn are calculated for n=pα ,pq, p2q, p2q2, pqr, p3q, p2qr, pqrs where p, q, r and s are distinct primes and a Sage math code is developed for designing graph and computing the indices. Conclusion: In the light of this study, it is possible to handle the other topological descriptors for computing and developing new algorithms for next studies and to study some spectrum and graph energies of certain finite rings with respect to PIS-graph easily.

中文翻译：

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Zn素理想和图的遗忘拓扑和维纳指数

背景：化学图论是数学化学的一个分支，假设分子的每个原子是一个顶点，原子之间的每个键是一条边。目的：由于该理论，可以避免化学分析的困难，因为分子的许多化学性质可以通过拓扑指数来确定和分析。由于这些参数，可以确定分子的物理化学性质、生物活性、环境行为和光谱性质。目前，利用拓扑指数研究Zn的零因子图是谱图论的一个热门领域。方法：对于具有恒等性的交换环R，R的素理想和图是顶点为R的非零真理想且两个不同顶点I和J相邻的图，当且仅当I+J是R的素理想时。结果：在本研究中，计算了 Zn 的素理想和图的遗忘拓扑指数和维纳指数，其中 n=pα ,pq, p2q, p2q2, pqr, p3q, p2qr, pqrs 其中 p, q, r 和 s 不同素数和 Sage 数学代码是为了设计图形和计算索引而开发的。结论：根据本研究，可以处理其他拓扑描述符以进行计算并为下一步研究开发新算法，并可以轻松地研究某些有限环相对于 PIS 图的谱和图能量。