It has book thickness 3 and queue number 2.

[4] It acts transitively on the vertices, on the edges and on the arcs of the graph.

[5] The characteristic polynomial of the Dyck graph is equal to

The Dyck graph is a toroidal graph, contained in the skeleton of a hexagonal regular map, {6,3}4,0, with 32 vertices, 48 edges, and 16 hexagonal cycles.

It is the dual of its symmetric toroidal embedding is the Shrikhande graph.

It can be visualized as net, a 4 by 4 array of hexagons, where left-right and top-bottom wrap into a flat torus.