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

Jehan Al-Bar, Ahmad Al-Kenani, Najat Muthana, Cheryl Praeger

Research output: Contribution to journalArticle

Abstract

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.
LanguageEnglish
Pages361-381
Number of pages21
JournalArs Mathematica Contemporanea
Volume12
Issue number2
StatePublished - 2017

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Oriented Graph
Quotient
Graph in graph theory
Vertex-transitive
Cycle
Group Action
Undirected Graph
Crossover
Consecutive
Internal
Invariant
Family

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Al-Bar, Jehan ; Al-Kenani, Ahmad ; Muthana, Najat ; Praeger, Cheryl. / A normal quotient analysis for some families of oriented four-valent graphs. In: Ars Mathematica Contemporanea. 2017 ; Vol. 12, No. 2. pp. 361-381
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A normal quotient analysis for some families of oriented four-valent graphs. / Al-Bar, Jehan; Al-Kenani, Ahmad; Muthana, Najat; Praeger, Cheryl.

In: Ars Mathematica Contemporanea, Vol. 12, No. 2, 2017, p. 361-381.

Research output: Contribution to journalArticle

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