On some distance-regular graphs with many vertices

Dean Crnkovic; Sanja Rukavina; Andrea Svob

paper

On some distance-regular graphs with many vertices

arXiv:1809.10197

Abstract

We construct distance-regular graphs, including strongly regular graphs, admitting a transitive action of the Chevalley groups $G_{2} (4)$ and $G_{2} (5)$ , the orthogonal group $O (7, 3)$ and the Tits group $T =$ $^{2} F_{4} (2)^{'}$ . Most of the constructed graphs have more than 1000 vertices, and the number of vertices goes up to 28431. Some of the obtained graphs are new.

18 pages