Rose window graphs underlying rotary maps

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 vertical bar i is an element of z(n)}. In this paper rotary maps on rose window graphs are considered. In particular, we answer the question posed in [S. Wilson, Rose window graphs, Ars Math. Contemp. 1 (2008), 7-19. http://amc.imfm.si/index.php/amc/issue/view/5] concerning which of these graphs underlie a rotary map. (C) 2010 Published by Elsevier B.V.