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05654613 Wusuying, Aishanjiang Negami, Seiya Yamamoto, Ko The distinguishing numbers of 4-regular quadrangulations on the Klein bottle. Yokohama Math. J. 55, No. 1, 71-92 (2009). 2009 Yokohama City University, Department of Mathematical Science, Yokohama; Yokohama National University, Faculty of Engineering, Department of Mathematics, Yokohama EN distingusihing quadrangulations Klein bottle A graph $G$ is said to be $d$-distinguishable if there is an assignment of $d$ labels to vertices such that no automorphism of $G$ other than the identity map preserves the labels of vertices. We shall prove that 4-regular quadrangulations on the Klein bottle are 2-distinguishable with few exceptions, after reviewing their classification.