The automorphism group of the comaximal graph of a commutative ring

Let [Formula: see text] be a commutative ring with nonzero identity. The comaximal graph of [Formula: see text], denoted by CG[Formula: see text], is a simple graph whose vertices are the elements of [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. The main purpose of this paper is to construct the automorphism groups (of some subgraphs) of CG[Formula: see text] and [Formula: see text] (or [Formula: see text] for short), where [Formula: see text] is the subgraph of [Formula: see text] which consists of non-unit elements of [Formula: see text] and [Formula: see text] is the Jacobson radical of [Formula: see text].