The Chromatic Number of the Square of a Halin Graph with Maximum Degree Five is Six

Abstract

This article proves that the square of a Halin graph $G$ with $\mathrm{\Delta }(G)=5$ has the chromatic number $6$. This gives a positive answer to an open problem in [Y. Wang, Distance two labelling of Halin graphs, Ars Combin. 114 (2014), 331–343].