On Sylow subgraphs of vertex-transitive self-complementary graphs

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33 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)531-533
Number of pages3
JournalBulletin of the London Mathematical Society
Volume31
Issue number5
DOIs
StatePublished - 1 Jan 1999
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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