Further Results on Locating Chromatic Number for Amalgamation of Stars Linking by One Path - A. Asmiati; Lyra Yulianti; C. Ike Tri Widyastuti (Indonesian Combinatorial Society (InaCombS), 2018)
Let G = (V, E) be a connected graph. Let c be a proper coloring using k colors, namely 1, 2, ⋯, k. Let Π = S1, S2, ⋯, Sk be a partition of V(G) induced by c and let Si be the color class that receives the color i. The color code, cΠ(v) = (d(v, S1), d(v, S2), ⋯, d(v, Sk)), where d(v, Si) = mind(v, x)∣x ∈ Si for i ∈ [1, k]. If all vertices in V(G) have different color codes, then c is called as the locating-chromatic k-coloring of G. Minimum k such that G has the locating-chromatic k-coloring is called the locating-chromatic number, denoted by χL(G). In this paper, we discuss the locating-chromatic number for n certain amalgamation of stars linking a path, denoted by nSk, m, for n ≥ 1, m ≥ 2, k ≥ 3, and k > m.