Geodesic
Two new infinite families of arc-transitive antipodal distance-regular graphs of diameter three with $\lambda =\mu $ related to groups $\mathrm{Sz}(q)$ and $^2G_2(q)$
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 4, pp. 1079-1087.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this paper, we construct two new infinite families of arc-transitive distance-regular graphs, related to Suzuki groups $Sz(q)$ and Ree groups $^2G_2(q)$, where $q>3$. They are antipodal $r$-covers of complete graphs on $q^2+1$ or $q^3+1$ vertices, respectively, with $\lambda =\mu $ and $r>1$ being an arbitrary odd divisor of $q-1$. We also find that the graph on the set of involutions of $Sz(q)$ with $q>3$, whose edges are the pairs of involutions $\{u,v\}$ such that $|uv|=5$, is distance-regular.
Classification : 05E18, 05E30, 05C12
Keywords: antipodal graph, arc-transitive graph, automorphism group, distance-regular graph, $r$-fold covering graph 
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     author = {Tsiovkina, L.Yu.},
     title = {Two new infinite families of arc-transitive antipodal distance-regular graphs of diameter three with $\lambda =\mu $ related to groups $\mathrm{Sz}(q)$ and $^2G_2(q)$},
     journal = {Journal of Algebraic Combinatorics},
     pages = {1079--1087},
     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2015__41_4_a4/}
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Tsiovkina, L.Yu. Two new infinite families of arc-transitive antipodal distance-regular graphs of diameter three with $\lambda =\mu $ related to groups $\mathrm{Sz}(q)$ and $^2G_2(q)$. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 4, pp. 1079-1087. http://geodesic.mathdoc.fr/item/JAC_2015__41_4_a4/