S-packing coloring of cubic Halin graphs

Given a non-decreasing sequence S= (s1, s2, …, sk) of positive integers, an S-packing coloring of a graph G is a partition of the vertex set of G into k subsets V1, V2, …, Vk such that for each 1≤i≤k, the distance between any two distinct vertices u and v in Vi is at least si+1. In this paper, we study the problem of S-packing coloring of cubic Halin graphs, and we prove that every cubic Halin graph is (1, 1, 2, 3) -packing colorable. In addition, we prove that such graphs are (1, 2, 2, 2, 2, 2) -packing colorable.