Classification of Edge-Transitive Rose Window Graphs

Given natural numbers n >= 3 and 1 <= a, r <= n-1, the rose window graph R(n)(a, r) is a quartic graph with vertex set {x(i)vertical bar i is an element of Z(n)} boolean OR {y(i)vertical bar i is an element of Z(n)} and edge set {{x(i), x(i+1)}vertical bar i is an element of Z(n)} boolean OR {{y(i), y(i+r)}vertical bar i is an element of Z(n)} boolean OR {{x(i), y(i)}vertical bar i is an element of Z(n)} boolean OR {{x(i+a), y(i)}vertical bar i is an element of Z(n)}. 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. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 216-231, 2010