We present enumerations of a class of maps on Klein bottle which give rise to semi-equivelar maps. Semi-equivelar maps are generalizations of equivelar maps. There are eleven types of semi-equivelar maps on the Klein bottle. These are of the types $\{ 3^{ 6}\}$, $\{ 4^{ 4}\}$, $\{ 6^{ 3}\}$, $\{ 3^{ 3},$ $4^{ 2}\}$, $\{ 3^{ 2},$ $4,$ $3,$ $4\}$, $\{ 3,$ $6,$ $3,$ $6\}$, $\{ 3^{ 4}, 6\}$, $\{ 4,$ $8^{ 2}\}$, $\{ 3, 12^{ 2}\}$, $\{ 4,$ $6,$ $12\}$, $\{ 3,$ $4,$ $6,$ $4\}$. In this article, we attempt to classify these maps.

Categories: math.CO math.GT

On enumeration of a class of maps on Klein bottle