2013/01/10 by Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco +1
Mathematics · #Adjacency matrix #Automorphism #Finite Group Theory Research #Graph theory and applications #Hermitian matrix #Quotient #Rings, Modules, and Algebras #Symmetric group #Transitive relation #Two-graph #Unitary state #Vertex-transitive graph #math.CO #msc:05C25
paper · pdf · doi:10.1007/s10801-012-0422-9
published as J. Algebraic Combinatorics 38 (2013), 745-765
openalex publication_date 2013/01/10 · arxiv created 2015/03/24 · arxiv updated 2015/03/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A finite graph Γ is called G-symmetric if G is a group of automorphisms of Γ which is transitive on the set of ordered pairs of adjacent vertices of Γ. 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 they 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.