On the locating chromatic number of trees

A palm S-n(a(1), a(2) , ... , a(n)) is simply a subdivision of a star S-n on every edge in ai - 1 times (for the ith-edge). In this paper, we derive some 'better' upper bound of the locating chromatic number of a tree by using the locating coloring of its composing palms. We also determine the locating chromatic number of a palm itself. We prove the complexity of the locating chromatic number of a regular palm tree Sn(k) and an olive S-n(1, 2, ... , n), namely X-L(S-n(k)) = Theta(n(1/k)); X-L(S-n(3)) = (1+o(1))(3)root 4n; and X-L(O-n) = [log(3) (n/4)] +3.