Abstract
The locating-chromatic number of a graph G can be defined as the cardinality of a minimum ordered partition Π of the vertex-set V(G) such that every two vertices in G have different coordinates with respect to Π and every two adjacent vertices in G are not in the same partition class in Π. In this case, the coordinate of a vertex v is defined as the distances from the vertex v to all partition classes in Π. In this paper, we discuss the locating-chromatic number of Halin graph, namely a planar graph H = T ⊎ C which constructed from a plane embedding of a tree T with at least four vertices, by connecting all the leaves of T (the vertices of degree 1) to form a cycle C that passes around the tree in the natural cyclic order defined by the embedding of the tree. In particular, we investigate the locating-chromatic number of the Halin graph H = T ⊎C, where T is a subdivision of a star and a double star.
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