The vertex-transitive and edge-transitive tetravalent graphs of square-free order

Cai-Heng Li; Z.P. Lu; G.X. Wang

doi:10.1007/s10801-014-0572-z

The vertex-transitive and edge-transitive tetravalent graphs of square-free order

Cai-Heng Li
, Z.P. Lu
, G.X. Wang

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

© 2014, Springer Science+Business Media New York. In this paper, a classification is given for tetravalent graphs of square-free order which are vertex-transitive and edge-transitive. It is shown that such graphs are Cayley graphs, edge-regular metacirculants and covers of some graphs arisen from simple groups $$\mathrm{A}_7$$A7, $$\mathrm{J}_1$$J1 and $$\mathrm{PSL}(2,p)$$PSL(2,p).

Original language	English
Pages (from-to)	25-50
Journal	Journal of Algebraic Combinatorics
Volume	42
Issue number	1
DOIs	https://doi.org/10.1007/s10801-014-0572-z
Publication status	Published - 2015

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abstract = "{\textcopyright} 2014, Springer Science+Business Media New York. In this paper, a classification is given for tetravalent graphs of square-free order which are vertex-transitive and edge-transitive. It is shown that such graphs are Cayley graphs, edge-regular metacirculants and covers of some graphs arisen from simple groups \$\$\textbackslash{}mathrm\{A\}\_7\$\$A7, \$\$\textbackslash{}mathrm\{J\}\_1\$\$J1 and \$\$\textbackslash{}mathrm\{PSL\}(2,p)\$\$PSL(2,p).",

author = "Cai-Heng Li and Z.P. Lu and G.X. Wang",

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AU - Li, Cai-Heng

AU - Lu, Z.P.

AU - Wang, G.X.

PY - 2015

Y1 - 2015

N2 - © 2014, Springer Science+Business Media New York. In this paper, a classification is given for tetravalent graphs of square-free order which are vertex-transitive and edge-transitive. It is shown that such graphs are Cayley graphs, edge-regular metacirculants and covers of some graphs arisen from simple groups $$\mathrm{A}_7$$A7, $$\mathrm{J}_1$$J1 and $$\mathrm{PSL}(2,p)$$PSL(2,p).

AB - © 2014, Springer Science+Business Media New York. In this paper, a classification is given for tetravalent graphs of square-free order which are vertex-transitive and edge-transitive. It is shown that such graphs are Cayley graphs, edge-regular metacirculants and covers of some graphs arisen from simple groups $$\mathrm{A}_7$$A7, $$\mathrm{J}_1$$J1 and $$\mathrm{PSL}(2,p)$$PSL(2,p).

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DO - 10.1007/s10801-014-0572-z

M3 - Article

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VL - 42

SP - 25

EP - 50

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

IS - 1

ER -

The vertex-transitive and edge-transitive tetravalent graphs of square-free order

Abstract

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