On the locating chromatic number of certain barbell graphs
Summary: 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.
scientific article; zbMATH DE number 7029958