On vertex-uniprimitive non-Cayley graphs of order pq

Mohammad A. Iranmanesh

On vertex-uniprimitive non-Cayley graphs of order pq

Group Theory 2014-07-18 v1 Combinatorics

Authors: Mohammad A. Iranmanesh

Abstract

Let $p$ and $q$ be distinct odd primes. Let $\Gamma=(V(\Gamma), E(\Gamma))$ be a non-Cayley vertex-transitive graph of order $pq.$ Let $G\leq \Aut(\Gamma)$ acts primitively on the vertex set $V(\Gamma)$ . In this paper, we show that $G$ is uniprimitive which is primitive but not 2-transitive and we obtain some information about $p, q$ and the minimality of the Socle $T=\soc(G).$

Keywords

vertex-transitive graphs non-Cayley graphs primitive groups uniprimitive order pq socle automorphism group

Cite

@article{arxiv.1407.4771,
  title  = {On vertex-uniprimitive non-Cayley graphs of order pq},
  author = {Mohammad A. Iranmanesh},
  journal= {arXiv preprint arXiv:1407.4771},
  year   = {2014}
}

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5 pages

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