New results of identifying codes in product graphs

Abstract For the vertex v of graph G and the subset N ⊆ V ( G ) of the vertex set, let I N ( v ) = { N ∩ N G [ v ] } . If, for all vertices v ’s of G , I N ( v ) ’s are distinct non-empty sets, then N is said to be an identifying code and we indicate it by i ( G ) . A graph G is called identifiable, if distinct vertices of this graph have distinct closed neighboods. In the current work, we investigate some upper bounds for the identifying code of given graph products.