Some properties of the comaximal graph of amalgamation of rings along an ideal

Let [Formula: see text] and [Formula: see text] be commutative rings with identity, [Formula: see text] be an ideal of [Formula: see text], and let [Formula: see text] be a ring homomorphism. The amalgamation of [Formula: see text] with [Formula: see text] along [Formula: see text] with respect to [Formula: see text] denoted by [Formula: see text], was introduced by D’Anna et al. in 2010. Recently, some properties of the comaximal graph of [Formula: see text] were studied by Shoar et al. In a graph [Formula: see text], the associated number [Formula: see text] is defined as the maximum distance of vertex [Formula: see text] to vertex [Formula: see text] such that [Formula: see text]. In this paper, we compare the values [Formula: see text] in the comaximal graph of [Formula: see text] and [Formula: see text] in the comaximal graph of [Formula: see text], where [Formula: see text]. Among other results, it is shown that the comaximal graph of [Formula: see text] is complemented (uniquely complemented) if and only if the comaximal graph of [Formula: see text] is complemented (uniquely complemented), provided that the Jacobson radical of [Formula: see text] contains [Formula: see text].