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


  • Jehan A. Al-bar King Abdulaziz University Jeddah, Saudi Arabia
  • Ahmad N. Al-kenani King Abdulaziz University Jeddah, Saudi Arabia
  • Najat M. Muthana King Abdulaziz University, Jeddah, Saudi Arabia
  • Cheryl E. Praeger University of Western Australia




Edge-transitive graph, oriented graph, cyclic quotient graph, transitive group


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 Marušič 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.

Author Biography

Cheryl E. Praeger, University of Western Australia

Also affiliated with King Abdulaziz University, Jeddah, Saudi Arabia