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 ∣ i ∈ Z n } ∪ { y i ∣ i ∈ Z n } and edge set { { x i , x i + 1 } ∣ i ∈ Z n } ∪ { { y i , y i + r } ∣ i ∈ Z n } ∪ { { x i , y i } ∣ i ∈ Z n } ∪ { { x i + a , y i } ∣ i ∈ 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.