On the rack homology of graphic quandles

This paper has partially a novel and partially a survey character. We start with a short review of rack (two term) homology of self distributive algebraic structures (shelves) and their connections to knot theory. We concentrate on a sub-family of quandles satisfying the graphic axiom. For a large family of graphic quandles (including infinite ones), we compute the second rack homology groups. Finally, we propose conjectures based on our computational data.