Robertson graph

In the mathematical field of graph theory, the Robertson graph or (4,5)-cage, is a 4-regular undirected graph with 19 vertices and 38 edges named after Neil Robertson. The Robertson graph is the unique (4,5)-cage graph and was discovered by Robertson in 1964. As a cage graph, it is the smallest 4-regular graph with girth 5. It has chromatic number 3, chromatic index 5, diameter 3, radius 3 and is both 4-vertex-connected and 4-edge-connected. It has book thickness 3 and queue number 2. The graph is neither planar nor 1-planar. The Robertson graph is also a Hamiltonian graph which possesses 5,376 distinct directed Hamiltonian cycles. The Robertson graph is one of the smallest graphs with cop number 4.