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Keywords:

  • group;
  • graph;
  • rose window;
  • vertex-transitive;
  • edge-transitive;
  • arc-transitive

Abstract

Given natural numbers n⩾3 and 1⩽a, rn−1, the rose window graph Rn(a, r) is a quartic graph with vertex set equation image and edge set equation image. In this article a complete classification of edge-transitive rose window graphs is given, thus solving one of the three open problems about these graphs posed by Steve Wilson in 2001. © 2010 Wiley Periodicals, Inc. J Graph Theory 65: 216–231, 2010