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ON SYLOW SUBGRAPHS OF VERTEX-TRANSITIVE SELF-COMPLEMENTARY GRAPHS

Published online by Cambridge University Press:  01 September 1999

MIKHAIL MUZYCHUK
MIKHAIL MUZYCHUK
Affiliation:
Department of Mathematics and Computer Science, Netanya Academic College, 42365 Netanya, Israel Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel
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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.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 5 , September 1999 , pp. 531 - 533
Copyright
© The London Mathematical Society 1999

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