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Browsing Math & Computer Science by Subject "Automorphism group"

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    On the automorphism groups of almost all circulant graphs and digraphs
    (Drustvo Matematikov, Fizikov in Astronomov, 2018) Bhoumik, Soumya; Dobson, Edward; Morris, Joy
    We attempt to determine the structure of the automorphism group of a generic circulant graph. We first show that almost all circulant graphs have automorphism groups as small as possible. The second author has conjectured that almost all of the remaining circulant (di)graphs (those whose automorphism group is not as small as possible) are normal circulant (di)graphs. We show this conjecture is not true in general, but is true if we consider only those circulant (di)graphs whose order is in a “large” subset of integers. We note that all non-normal circulant (di)graphs can be classified into two natural classes (generalized wreath products, and deleted wreath type), and show that neither of these classes contains almost every non-normal circulant digraph.
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    Strongly regular edge-transitive graphs
    (Drustvo Matematikov, Fizikov in Astronomov, 2009) Morris, Joy; Praeger, Cheryl E.; Spiga, Pablo
    In this paper, we examine the structure of vertex- and edge-transitive strongly regular graphs,using normal quotient reduction. We show that their reducible graphs in this family have quasi primitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parameters of the graphs in this family that reduce to complete graphs