Structure of the maximal -local geometry point-line collinearity graph

Abstract

The point-line collinearity graph${\mathcal{G}}$of the maximal 2-local geometry for the largest simple Fischer group,$Fi_{24}^{\prime }$, is extensively analysed. For an arbitrary vertex$a$of${\mathcal{G}}$, the$i\text{th}$-disc of$a$is described in detail. As a consequence, it follows that${\mathcal{G}}$has diameter$5$. The collapsed adjacency matrix of${\mathcal{G}}$is given as well as accompanying computer files which contain a wealth of data about${\mathcal{G}}$.Supplementary materials are available with this article.