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.