Upper Bounds of the Locating Chromatic Numbers of Shadow Cycle Graphs

If G is a connected finite simple graph with its vertices properly colored with k colors appearing, then with respect to an ordering of the colors, to each vertex v a k-tuple can be assigned whose entries give the distances in G from v to the different color sets. The locating chromatic number (lcn) of G is the smallest k for which a proper vertex coloring of G with k colors appearing exists such that the corresponding k-tuples are distinct. In this paper we obtain by construction upper bounds on the lcns of shadow cycle graphs.