Unitary graphs, and classification of a family of symmetric graphs with complete quotients
by A/Prof Sanming Zhou
Abstract: A finite graph is called symmetric if its automorphism group is transitive on the set of arcs (ordered pairs of adjacent vertices) of the graph. This is to say that all arcs have the same status in the graph. I will talk about a family of symmetric graphs, called the unitary graphs, whose vertices are flags of the Hermitian unital (a special block design) 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 our classification of a family of symmetric graphs with complete quotients. I will also talk about this classification and some combinatorial properties of the unitary graphs. This talk is based on joint work with M. Giulietti, S. Marcugini and F. Pambianco.
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