  An automorphism of a graph describes its structural symmetry and the concept
of fixing number of a graph is used for breaking its symmetries (except the
trivial one). In this paper, we evaluate automorphisms of the co-normal product
graph $G_1\ast G_2$ of two simple graphs $G_1$ and $G_2$ and give sharp bounds
on the order of its automorphism group. We study the fixing number of $G_1\ast
G_2$ and prove sharp bounds on it. Moreover, we compute the fixing number of
the co-normal product of some families of graphs.

Combinatorics