10 - Individual graph descriptions

Summary

In this chapter, we describe the sporadic rank 3 graphs, and further interesting strongly regular graphs that have special properties not shared by the other graphs in the infinite families to which they belong. Part of the information given here was obtained using the computer algebra system GAP and its package GRAPE(with Nauty). Among the listed properties one finds (various) constructions, a discussion of the maximal cliques and cocliques, a table with regular sets arising from a group action,local characterizations, sporadic properties such as connections with Ramsey numbers, chromatic number, p-ranks, decompositions, etc. The chapter has exactly 100 sections, mostly each dealing with an individual graph, but often also discussing a small family of graphs with equally many vertices (ranging from 5 to 531441 vertices). It contains some new geometric and/or combinatorial constructions of a few sporadic (exceptional and extraspecial) rank 3 graphs.