### Abstract

Language | English |
---|---|

Pages | 361-381 |

Number of pages | 21 |

Journal | Ars Mathematica Contemporanea |

Volume | 12 |

Issue number | 2 |

State | Published - 2017 |

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### Cite this

*Ars Mathematica Contemporanea*,

*12*(2), 361-381.

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*Ars Mathematica Contemporanea*, vol. 12, no. 2, pp. 361-381.

**A normal quotient analysis for some families of oriented four-valent graphs.** / Al-Bar, Jehan; Al-Kenani, Ahmad; Muthana, Najat; Praeger, Cheryl.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A normal quotient analysis for some families of oriented four-valent graphs

AU - Al-Bar,Jehan

AU - Al-Kenani,Ahmad

AU - Muthana,Najat

AU - Praeger,Cheryl

PY - 2017

Y1 - 2017

N2 - We analyse the normal quotient structure of several infinite families of finite connected edge-transitive, four-valent oriented graphs. These families were singled out by Marusic and others to illustrate various different internal structures for these graphs in terms of their alternating cycles (cycles in which consecutive edges have opposite orientations). Studying the normal quotients gives fresh insights into these oriented graphs: in particular we discovered some unexpected ‘cross-overs’ between these graph families when we formed normal quotients. We determine which of these oriented graphs are ‘basic’, in the sense that their only proper normal quotients are degenerate. Moreover, we show that the three types of edge-orientations studied are the only orientations, of the underlying undirected graphs in these families, which are invariant under a group action which is both vertex-transitive and edge-transitive.

AB - We analyse the normal quotient structure of several infinite families of finite connected edge-transitive, four-valent oriented graphs. These families were singled out by Marusic and others to illustrate various different internal structures for these graphs in terms of their alternating cycles (cycles in which consecutive edges have opposite orientations). Studying the normal quotients gives fresh insights into these oriented graphs: in particular we discovered some unexpected ‘cross-overs’ between these graph families when we formed normal quotients. We determine which of these oriented graphs are ‘basic’, in the sense that their only proper normal quotients are degenerate. Moreover, we show that the three types of edge-orientations studied are the only orientations, of the underlying undirected graphs in these families, which are invariant under a group action which is both vertex-transitive and edge-transitive.

M3 - Article

VL - 12

SP - 361

EP - 381

JO - Ars Mathematica Contemporanea

T2 - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

SN - 1855-3974

IS - 2

ER -