A subset S of vertices of a graph G is a determining set for G if every automorphism of G is uniquely determined by its action on S. The determining number of a graph G is the smallest integer r such that G has a determining set of size r. In this paper, we study the determining number of edge-corona product, hierarchical product of graphs and the determining number of blow-up of some graphs. Also, we investigate the determining number of the zero divisor graph of the ring Zn, for some values of n.
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Afkhami et al. (2024) studied this question.
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