Robertson graph
Introduction 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 Robertson graph is also a Hamiltonian graph which possesses  distinct directed Hamiltonian cycles.The Robertson graph is one of the smallest graphs with cop number 4.
Algebraic properties 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 is::
Gallery Image:Robertson graph.svg|The Robertson graph as drawn in the original publication.Image:Robertson graph 3COL.svg|The chromatic number of the Robertson graph is 3.Image:Robertson graph 5color edge.svg|The chromatic index of the Robertson graph is 5.
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