$S$-Packing Coloring of Cubic Halin Graphs

Given a non-decreasing sequence $S = (s{1}, s{2}, \ldots , s{k})$ of positive integers, an $S$-packing coloring of a graph $G$ is a partition of the vertex set of $G$ into $k$ subsets ${V{1}, V{2}, \ldots , V{k}}$ such that for each $1 \leq i \leq k$, 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.