LAUSR

The coprime graph is a graph $$TCG_n$$TCGn whose vertex set is $$\{1, 2, 3,\ldots ,n\}$${1,2,3,…,n}, with two vertices i and j joined by an edge if and only if $$\hbox {gcd}(i, j)= 1$$gcd(i,j)=1. In this paper we first determine the full automorphism group of the coprime graph, and then find the regularities for a set becoming a determining set or a resolving set in a coprime graph. Finally, we show that minimal determining sets of coprime graphs satisfy the exchange property and minimal resolving sets of coprime graphs do not satisfy the exchange property.