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.