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  • Bridging semisymmetric and half-arc-transitive actions on graphs
    Marušič, Dragan ; Potočnik, Primož, 1971-
    A generalization of some of the Folkman's constructions of the so called semisymmetric graphs, that is regular graphs which are edge- but not vertex-transitive, was given recently, together with a ... natural connection of graphs admitting 1/2-arc-transitive group actions and certain graphs admitting semisymmetric group actions. This connection is studied in more detail in this paper. A sufficient condition for the semisymmetry of the so called generalized Folkman graphs arising from certain graphs admitting a 1/2-arc transitive group action is given. Furthermore, the concepts of alter-sequence and alter-exponent is introduced and studied in great detail and then used to study the interplay of three classes of graphs: cubic graphs admitting a one-regular group action, the corresponding line graphs which admit a 1/2-arc-transitive action of some group and the associated generalized Folkman graphs. At the end an open problem is posed, suggesting an in-depth analysis of the structure of tetravalent 1/2-arc-transitive graphs with alter-exponent 2.
    Type of material - book ; adult, serious
    Publication and manufacture - Ljubljana : Institute of Mathematics, Physics and Mechanics, Department of Mathematics, 2001
    Language - english
    COBISS.SI-ID - 14729987

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