  The weighted dual graph of a two-dimensional normal singularity $(X, x)$
represents the topological nature of the exceptional locus of its minimal log
resolution. $(X, x)$ and its graph are said to be taut if the singularity can
be uniquely determined by the graph. Laufer gave a complete list of taut
singularities over $\mathbb{C}$. In positive characteristics, taut graphs over
$\mathbb{C}$ are not necessarily taut and tautness have been studied only for
special cases. In this paper, we prove the tautness of $F$-regular
singularities. We also discuss the tautness of $F$-pure rational singularities.
