Graph invariants provide an outstanding tool for investigation of abstract structures of graphs. They contain global and general information about a graph and its particular substructures. In this paper, the graph invariants such as vertex connectivity, metric dimension, minimum vertex degree, independence number, domination number, Laplacian energy and Zagreb indices of line graph of zero-divisor graph over the rings \(\mathbb {Z}_{pq}\) and \(\mathbb {Z}_{p^n}\) (where p and q are prime) are determined. Moreover, we provide a MATLAB code for calculating Laplacian energy and Zagreb indices of line graph of \(\varGamma (\mathbb {Z}_{n})\).

图不变量为研究图的抽象结构提供了一种出色的工具。它们包含有关图及其特定子结构的全局和一般信息。在本文中，零因数图在环上的线图的顶点连通性、度量维数、最小顶点度、独立数、支配数、拉普拉斯能量和萨格勒布指数等图不变量\(\mathbb {Z}_{ pq}\)和\(\mathbb {Z}_{p^n}\)（其中p和q是素数）被确定。此外，我们提供了一个 MATLAB 代码，用于计算\(\varGamma (\mathbb {Z}_{n})\)的线图的拉普拉斯能量和萨格勒布指数。