The non-collinearity graph of the \(O^+(8,2)\) quadric is uniquely geometrisable
The non-collinearity graph of the \(O^+(8,2)\) quadric is the graph whose vertex set consists of the points of the \(O^+(8,2)\) polar space, and two vertices are adjacent in this graph if and only if the corresponding points are non-collinear in the polar space. In this paper, the author shows that there is a unique partial geometry \(\text{pg}(8,7,4)\) whose point graph is this graph, and the author also demonstrates that this geometry has the affine plane of order 3 as a subgeometry.
scientific article; zbMATH DE number 1515345