High Quality Content by WIKIPEDIA articles! 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. The Robertson graph is also a Hamiltonian graph which possesses 5,376 distinct directed Hamiltonian cycles.

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