Further Results on Locating Chromatic Number for Amalgamation of Stars Linking by One Path

Abstract

Let G = (V,E) be a connected graph. Let c be a proper coloring using k colors, namely 1, 2,·s, k. Let P ={S 1, S 2,..., S k } be a partition of V(G) induced by c and let S i be the color class that receives the color i. The color code, c P (v)=(d(v,S 1), d(v,S 2),...,d(v,S k)), where d(v,S i)=min {d(v,x)|x Î S i } for i Î [1,k]. If all vertices in V(G) have different color codes, then c is called as the \emphlocating-chromatic k-coloring of G. Minimum k such that G has the locating-chromatic k-coloring is called the locating-chromatic number, denoted by c L (G). In this paper, we discuss the locating-chromatic number for n certain amalgamation of stars linking a path, denoted by nS k,m, for n ≥ 1, m ≥ 2, k ≥ 3, and k>m.