• Title, Summary, Keyword: vertex-transitive graph

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GENERALIZED CAYLEY GRAPHS OF RECTANGULAR GROUPS

  • ZHU, YONGWEN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.4
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    • pp.1169-1183
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    • 2015
  • We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.

SEMISYMMETRIC CUBIC GRAPHS OF ORDER 34p3

  • Darafsheh, Mohammad Reza;Shahsavaran, Mohsen
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.739-750
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    • 2020
  • A simple graph is called semisymmetric if it is regular and edge transitive but not vertex transitive. Let p be a prime. Folkman proved [J. Folkman, Regular line-symmetric graphs, Journal of Combinatorial Theory 3 (1967), no. 3, 215-232] that no semisymmetric graph of order 2p or 2p2 exists. In this paper an extension of his result in the case of cubic graphs of order 34p3, p ≠ 17, is obtained.