H(n)-Gordian graphs of knotoids

In this talk, we discuss the Gromov hyperbolicity of H(n)-Gordian graphs of knotoids. We provide a proof of the non-hyperbolicity of the H(n)-Gordian graphs of knotoids using the Gromov four-point condition. Additionally, we analyze the quotient graphs obtained by identifying knotoids with the same values of certain invariants, such as the height of knotoids and the span of the Affine index polynomial. We show that these quotient graphs are complete and hence 0-hyperbolic.