On the locating chromatic number of some Buckminsterfullerene-type graphs
Yolanda Putri, Lyra Yulianti, Yanita Yanita · Journal of Physics Conference Series · 2021
Abstract Let G = (V, E) be a nontrivial graph and k be a positive integer. Let c : V(G) → {1,2,3,…,k} be a vertex coloring of G such that if uv ∈ E(G) then c(u) ≠ c(v). For 1 ≤ i ≤ k, let Si be the ith set of vertices given color i and define Π = {S1 ,S2 ,…,Sk }. The color code of a vertex v ∈ V (G), denoted by cπ(v), is defined as the ordered k-tuple cπ(v) = (d(v, S1 ), d(v, S2), … , d(v, S k)), where d(v, Si) = min{d(v, x) | x ∈ Si} for 1 ≤ i ≤ k. If every two vertices u and v in G have different color codes, then c is defined as the locating k-coloring of G. The minimum number of color used in the locating k-coloring of G is defined as the locating chromatic number of G, denoted by XL(G). This paper determined the locating chromatic number of some Buckminsterfullerene-type graph and some (4, 6)-fullerene graphs.