Enumeration of doubly semi-equivelar maps on the Klein bottle

Avertexv inamapM hastheface-sequence(pn1 1 .pn2 2 .....pnk
k ),if consecutive ni numbers of pi-gons are incident at v in the given cyclic order for 1 ≤ i ≤ k. A map is called semi-equivelar if the face-sequence of each vertex is same throughout the map. A doubly semi-equivelar map is a generalization of semi-equivelar map
which has precisely 2 distinct face-sequences. In this article, we determine all the types of doubly semi-equivelar maps of combinatorial curvature 0 on the Klein bottle. We present classification of doubly semi-equivelar maps on the Klein bottle and illustrate this classification for those doubly semi-equivelar maps which comprise of face-sequence pairs {(36),(33.42)} and {(33.42),(44)}