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.
