Twisted right-angled Artin groups embedded in knot groups

Twisted right-angled Artin groups are defined through presentation based on mixed graphs. Each vertex corresponds to a generator, each undirected edge yields a commuting relation and each directed edge gives a Klein bottle relation. If there is no directed edge, then this reduces to an ordinary right-angled Artin group. There is a characterization of right-angled Artin groups which can be embedded in knot groups by Katayama. In this paper, we completely determine twisted right-angled Artin groups embedded in knot groups.