Bounds on Identifying Codes in the Cartesian Product of a Star and a Path Graph

Abstract

In a graph, an identifying code (or ID code, for short) is a dominating set with the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. Thus every vertex can be uniquely identified by this intersection. The ID code number of a graph G is the minimum cardinality of an ID code of G and is denoted by γID(G). We present lower and upper bounds for γID in the Cartesian product of star and path graphs.