Valency seven symmetric graphs of order 2 p q

Xiao-Hui Hua; Li Chen

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 3, page 581-599
  • ISSN: 0011-4642

Abstract

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A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, all connected valency seven symmetric graphs of order 2 p q are classified, where p , q are distinct primes. It follows from the classification that there is a unique connected valency seven symmetric graph of order 4 p , and that for odd primes p and q , there is an infinite family of connected valency seven one-regular graphs of order 2 p q with solvable automorphism groups, and there are four sporadic ones with nonsolvable automorphism groups, which is 1 , 2 , 3 -arc transitive, respectively. In particular, one of the four sporadic ones is primitive, and the other two of the four sporadic ones are bi-primitive.

How to cite

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Hua, Xiao-Hui, and Chen, Li. "Valency seven symmetric graphs of order $2pq$." Czechoslovak Mathematical Journal 68.3 (2018): 581-599. <http://eudml.org/doc/294737>.

@article{Hua2018,
abstract = {A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, all connected valency seven symmetric graphs of order $2pq$ are classified, where $p$, $q$ are distinct primes. It follows from the classification that there is a unique connected valency seven symmetric graph of order $4p$, and that for odd primes $p$ and $q$, there is an infinite family of connected valency seven one-regular graphs of order $2pq$ with solvable automorphism groups, and there are four sporadic ones with nonsolvable automorphism groups, which is $1,2,3$-arc transitive, respectively. In particular, one of the four sporadic ones is primitive, and the other two of the four sporadic ones are bi-primitive.},
author = {Hua, Xiao-Hui, Chen, Li},
journal = {Czechoslovak Mathematical Journal},
keywords = {arc-transitive graph; symmetric graph; $s$-regular graph},
language = {eng},
number = {3},
pages = {581-599},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Valency seven symmetric graphs of order $2pq$},
url = {http://eudml.org/doc/294737},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Hua, Xiao-Hui
AU - Chen, Li
TI - Valency seven symmetric graphs of order $2pq$
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 581
EP - 599
AB - A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, all connected valency seven symmetric graphs of order $2pq$ are classified, where $p$, $q$ are distinct primes. It follows from the classification that there is a unique connected valency seven symmetric graph of order $4p$, and that for odd primes $p$ and $q$, there is an infinite family of connected valency seven one-regular graphs of order $2pq$ with solvable automorphism groups, and there are four sporadic ones with nonsolvable automorphism groups, which is $1,2,3$-arc transitive, respectively. In particular, one of the four sporadic ones is primitive, and the other two of the four sporadic ones are bi-primitive.
LA - eng
KW - arc-transitive graph; symmetric graph; $s$-regular graph
UR - http://eudml.org/doc/294737
ER -

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