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2 results

  • ON SYLOW SUBGRAPHS OF VERTEX-TRANSITIVE SELF-COMPLEMENTARY GRAPHS

  • MIKHAIL MUZYCHUK
  • Journal:
    Bulletin of the London Mathematical Society / Volume 31 / Issue 5 / September 1999
    Published online by Cambridge University Press:
    01 September 1999, pp. 531-533
    Print publication:
    September 1999

  • One of the basic facts of group theory is that each finite group contains a Sylow p-subgroup for each prime p which divides the order of the group. In this note we show that each vertex-transitive self-complementary graph has an analogous property. As a consequence of this fact, we obtain that each prime divisor p of the order of a vertex-transitive self-complementary graph satisfies the congruence pm ≡ 1(mod 4), where pm is the highest power of p which divides the order of the graph.