Abstract
In this article, graph blow-up is used to study the implements of the co-maximal graph and the co-maximal ideal graph 𝒞(R) of a commutative ring R. We show that for a ring R with finitely many maximal ideals, the graph 𝒞(R) is a blow-up of a Boolean graph, and we give more detailed structure of the graphs and 𝒞(R) as blow-ups of Boolean graphs. We determine for what rings R, 𝒞(R) or is a finite graph, respectively. In the end, we get some new results for rings by taking advantage of the graph .
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