S-Packing Coloring of Cubic Halin Graphs

09/19/2022

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by   Batoul Tarhini, et al.

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Given a non-decreasing sequence S = (s_1, s_2, … , s_k) of positive integers, an S-packing coloring of a graph G is a partition of the vertex set of G into k subsets {V_1, V_2, … , V_k} such that for each 1 ≤ i ≤ k, the distance between any two distinct vertices u and v in V_i is at least s_i + 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.