‎Distinguishing index of Kronecker product of two graphs - ‎Saeid Alikhani; Samaneh Soltani (Electronic Journal of Graph Theory and Applications (EJGTA), 2021)
The distinguishing index D'(G)  of a graph G is the least integer d such that G has an edge labeling with d labels that is preserved only by a trivial automorphism. The Kronecker product G x H of two graphs G and H is the graph with vertex set V(G) x V(H) and edge set {{(u,x), (v,y)} |{u,v} ∈ E(G) and {x,y} ∈  E(H)}. In this paper we study the distinguishing index of Kronecker product of two graphs.