Rose window graphs underlying rotary maps

Abstract

Given natural numbers ▫$n ge 3$▫ and ▫$1 le a$▫, ▫$r le n-1$▫, the rose window graph ▫$R_n(a,r)$▫ is a quartic graph with vertex set ▫${x_i verti in {mathbb Z}_n } cup {y_i verti in {mathbb Z}_n }$▫ and edge set ▫${{x_i, x_{i+1}} verti in {mathbb Z}_n } cup {{y_i, y_{i+1}} verti in {mathbb Z}_n } cup {{x_i, y_i} verti in {mathbb Z}_n} cup {{x_{i+a}, y_i} verti in {mathbb Z}_n }$▫. 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