The ruby graph is the 18-vertex, 27-edge cubic Hamiltonian graph illustrated above. It has girth 5, graph crossing number 1, graph diameter 4, and chromatic number 3. It is also an apex graph.
The name appears to refer to the faceted gemstone-like visual appearance of the graph in the embedding presented by Robertson et al. (2019, Fig. 4).
A cubic graph is cyclically 5-connected if it has girth at least 5 and every edge cut separating two subgraphs that contain cycles has at least five edges.
The characterization of cyclically 5-connected nonplanar cubic graphs states that such a graph is not planar if and only if it contains at least one of the Petersen graph, triplex graph, box graph, and ruby graph as a topological minor (Robertson et al. 2019).
The ruby graph is implemented in the Wolfram Language as GraphData["RubyGraph"].
