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={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, cP(v)=(d(v,S1), d(v,S2),...,d(v,Sk)), where d(v,Si)=min {d(v,x)|x Î Si} 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 cL(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.

Keywords

• locating chromatic number, amalgamation of stars