Israel Journal of Mathematics

, Volume 205, Issue 1, pp 35–72 | Cite as

Characterising vertex-star transitive and edge-star transitive graphs

  • Michael Giudici
  • Cai Heng Li
  • Ákos Seress
  • Anne Thomas
Article

Abstract

Recent work of Lazarovich provides necessary and sufficient conditions on a graph L for there to exist a unique simply-connected (k,L)-complex. The two conditions are symmetry properties of the graph, namely vertexstar transitivity and edge-star transitivity. In this paper we investigate vertex- and edge-star transitive graphs by studying the structure of the vertex and edge stabilisers of such graphs. We also provide new examples of graphs that are both vertex-star transitive and edge-star transitive.

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Copyright information

© Hebrew University of Jerusalem 2015

Authors and Affiliations

  • Michael Giudici
    • 1
  • Cai Heng Li
    • 1
  • Ákos Seress
    • 2
  • Anne Thomas
    • 2
  1. 1.School of Mathematics and StatisticsThe University of Western AustraliaCrawleyAustralia
  2. 2.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK

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