Robertson graph
In the mathematical field of graph theory, the Robertson graph or -cage, is a 4-regular undirected graph with 19 vertices and 38 edges named after Neil Robertson.
The Robertson graph is the unique -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 Robertson graph is also a Hamiltonian graph which possesses distinct directed Hamiltonian cycles.The Robertson graph is not a vertex-transitive graph and its full automorphism group is isomorphic to the dihedral group of order 24, the group of symmetries of a regular dodecagon, including both rotations and reflections.
The characteristic polynomial of the Robertson graph isGallery
