Unexpected symmetries in unstable graphs
Journal of Combinatorial Theory Series B
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The present paper investigates arc-transtive graphs in terms of their stability, and shows, somewhat contrary to expectations, that the property of instability is not as rare as previously thought. Until quite recently, the only known example of a finite, arc-transitive vertex-determining unstable graph was the underlying graph of the dodecahedron. This paper illustrates some methods for constructing finite arc-transitive unstable graphs, and three infinite families of such graphs are given as applications. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 95–110, 2001