Geodesic
Unitary graphs and classification of a family of symmetric graphs with complete quotients
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 3, pp. 745-765.

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

Summary: A finite graph $\Gamma $ is called G-symmetric if G is a group of automorphisms of $\Gamma $ which is transitive on the set of ordered pairs of adjacent vertices of $\Gamma $. We study a family of symmetric graphs, called the unitary graphs, whose vertices are flags of the Hermitian unital and whose adjacency relations are determined by certain elements of the underlying finite fields. Such graphs admit the unitary groups as groups of automorphisms, and play a significant role in the classification of a family of symmetric graphs with complete quotients such that an associated incidence structure is a doubly point-transitive linear space. We give this classification in the paper and also investigate combinatorial properties of the unitary graphs.
Keywords: symmetric graph, arc-transitive graph, unitary group, Hermitian unital, linear space, unitary graph 
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     title = {Unitary graphs and classification of a family of symmetric graphs with complete quotients},
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Giulietti, Massimo; Marcugini, Stefano; Pambianco, Fernanda; Zhou, Sanming. Unitary graphs and classification of a family of symmetric graphs with complete quotients. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 3, pp. 745-765. http://geodesic.mathdoc.fr/item/JAC_2013__38_3_a0/