The Full Automorphism Groups, Determining Sets and Resolving Sets of Coprime Graphs

The coprime graph is a graph T C G n whose vertex set is { 1 , 2 , 3 , … , n } , with two vertices i and j joined by an edge if and only if 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.