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

Abstract

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.