The palette index of Sierpiński triangle graphs and Sierpiński graphs

The palette of a vertex $v$ of a graph $G$ in a proper edge coloring is the set of colors assigned to the edges which are incident to $v$. The palette index of $G$ is the minimum number of palettes occurring among all proper edge colorings of $G$. In this paper, we consider the palette index of Sierpiński graphs $S_p^n$ and Sierpiński triangle graphs $\widehat{S}_3^n$. In particular, we determine the exact value of the palette index of Sierpiński triangle graphs. We also determine the palette index of Sierpiński graphs $S_p^n$ where $p$ is even, $p=3$, or $n=2$ and $p=4l+3$.