On Locating Chromatic Number of Cubic Graph with Tree Cycle, Cn,2n,n, for n=3,4,5

Abstract

Let G = (V(G), E(G)) be a connected graph and is coloring of graph G. Let Π = {C 1, C 2, …,Ck }, where Ci is the partition of the vertex in which is colored i with 1 ≥ i ≥ k. The representation v for Π is called the color code, denoted C Π(v) is a ordered pair with k-element namely, C Π(v) = (d(v, C 1), d(v, C 2), …, d(v, Ck )), where d(v, Ci )= mind{d(v, x)|xεCi } for 1 ≥ i ≥ k. If every vertex in G have different color code, the c is locating coloring. The minimum number of colors used in G is called chromatic locating, notated by XL (G). In this paper, we will determine the locating coloring of graph cubic Cn,2n,n , for n=3,4,5.