The Goddard-Henning graph, illustrated above in several embeddings, is the 9-node planar graph of graph diameter 2 having domination number . It was first constructed by MacGillivray and Seyffarth (1996) and subsequently proved (Goddard and Henning 2002, Henning and Yeo 2013, pp. 55-56) to be the unique diameter-2 planar graph with ; all other diameter-2 planar graphs have domination number at most 2.
It is the skeleton of the Goddard-Henning enneahedron.
The Goddard-Henning graph can be obtained from the generalized quadrangle by deleting two edges and hence is a unit-distance graph.
It is also self-dual.