Dirac semimetals lack stable surface Fermi arcs. However, they can exhibit a bulk-hinge correspondence: when terminated in rod geometry, zero energy arclike states appear on the hinges connecting projections of bulk points. In this work, authors derive symmetry indicators that determine existence higher-order arcs for general groups. The results show points with linear dispersion all directions...

In 1963, Tibor Gallai [9] asked whether every strongly connected directed graph D is spanned by α directed circuits, where α is the stability of D. We give a proof of this conjecture. 1 Coherent cyclic orders. In this paper, circuits of length two are allowed. Since loops and multiple arcs play no role in this topic, we will simply assume that our digraphs are loopless and simple. A directed gr...