On the Locating Chromatic Number of Certain Barbell Graphs

Abstract EN

The locating chromatic number of a graph G is defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are not contained in the same partition class.

In this case, the coordinate of a vertex v in G is expressed in terms of the distances of v to all partition classes.

This concept is a special case of the graph partition dimension notion.

In this paper we investigate the locating chromatic number for two families of barbell graphs.