Design theory
Finite geometries
On 2-arc-transitive covers of complete graphs
Journal of Combinatorial Theory Series B
Imprimitive symmetric graphs, 3-arc graphs and 1-designs
Discrete Mathematics - Algebraic and topological methods in graph theory
Finite symmetric graphs with two-arc transitive quotients
Journal of Combinatorial Theory Series B
A Local Analysis of Imprimitive Symmetric Graphs
Journal of Algebraic Combinatorics: An International Journal
On a class of finite symmetric graphs
European Journal of Combinatorics
Imprimitive symmetric graphs with cyclic blocks
European Journal of Combinatorics
Discrete Applied Mathematics
Unitary graphs and classification of a family of symmetric graphs with complete quotients
Journal of Algebraic Combinatorics: An International Journal
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We find a natural construction of a large class of symmetric graphs from point- and block-transitive 1-designs. The graphs in this class can be characterized as G-symmetric graphs whose vertex sets admit a G-invariant partition B of block size at least 3 such that, for any two blocks B, C of B either there is no edge between B and C, or there exists only one vertex in B not adjacent to any vertex in C. The special case where the quotient graph ΓB of Γ relative to B is a complete graph occurs if and only if the 1-design needed in the construction is a G-doubly transitive and G-block-transitive 2-design, and in this case we give an explicit classification of Γ when G is a doubly transitive projective group or an affine group containing the affine general group. Examples of such graphs include cross ratio graphs studied recently by Gardiner, Praeger and Zhou and some other graphs with vertices the (point, line)-flags of the projective or affine geometry.