Abstract: Let $\phi: G\rightarrow S$ be a 2-cell embedding of a graph $G$ into a surface $S$. If all faces of $G$ are consecutively adjacent, equivalently the dual graph of the embedded graph $G$ contains a Hamilton circuit, then the embedding $\phi$ is said to be a consecutively adjacent face embedding. In this paper the authors study the maximum genus of a graph that admits a consecutively adjacent face embedding in the Klein Bottle.

Key words: Maximum Genus, Upper Embeddable, Deficiency Number, Klein Bottle