Assume that R is a commutative ring with non-zero identity and \(W^*(R)\) is the set of all non-zero non-unit elements of R. Also, for \(x\in R\), the ideal which is generated by x, is denoted by Rx. The cozero-divisor graph of R, which is denoted by \(\Gamma '(R)\), is a graph with \(W^*(R)\) as the vertex-set, and two distinct vertices x and y are adjacent in \(W^*(R)\) if and only if \(x\notin Ry\) and \(y\notin Rx\). In this paper, we completely determine all finite commutative rings R such that \(\Gamma '(R)\) is a line graph. We also characterize all finite commutative rings R such that \(\Gamma '(R)\) is isomorphic to its line graph.

假设R是具有非零恒等式的交换环，并且\(W^*(R)\)是R的所有非零非单位元素的集合。此外，对于\(x\in R\) ，由x生成的理想值用Rx表示。R的余零除数图，用\(\Gamma '(R)\)表示，是以\(W^*(R)\)作为顶点集，并且有两个不同的顶点x和y在\(W^*(R)\)中相邻当且仅当\(x\notin Ry\)和\(y\notin Rx\)。在本文中，我们完全确定所有有限交换环R使得\(\Gamma '(R)\)是一个线图。我们还表征所有有限交换环R，使得\(\Gamma '(R)\)与其线图同构。