On automorphisms and fixing number of co-normal product of graphs.

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 ∗ 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 ∗ G 2 and prove sharp bounds on it. Moreover, we compute the fixing number of the co-normal product of some families of graphs. [ABSTRACT FROM AUTHOR]