### Distinguishing index of Kronecker product of two graphs

#### Abstract

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.

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PDFDOI: http://dx.doi.org/10.5614//ejgta.2021.9.1.7

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