The locating-chromatic number for Halin graphs

Let G be a connected graph. Let f be a proper k-coloring of G and Π = {R1, R2, . . . , Rk} be an ordered partition of V (G) into color classes. For any vertex v of G, define the color code cΠ(v) of v with respect to Π to be a ktuple (d(v, R1), d(v, R2), . . . , d(v, Rk)), where d(v, Ri) = min{d(v, x)|x ∈ Ri}. If distinct vertices have distinct color codes, then we call f a locating coloring of G. The locating-chromatic number of G is the minimum number k such that G admits a locating coloring with k colors. In this paper, we determine a lower bound of the locating-chromatic number of Halin graphs. We also give the locating-chromatic number of a Halin graph of a double star.