Let $R$ be a commutative ring with non-zero identity. The comaximal graph is a graph with vertices all elements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $Rx +Ry = R$. Let $\Gamma_2(R)$ be the subgraph of the comaximal graph with vertex-set $W^{*}(R)$, where $W^{*}(R)$ is the set of all non-zero and non-unit elements of $R$. In this paper, we investigate when the graph $\Gamma_2(R)$ is a line graph. We completely present all commutative rings which their comaximal graphs are line graphs. Also, we study when the comaximal graph is the complement of a line graph.
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