In this paper we define a characteristic of toroidal graphs called the handle number. The handle number is the minimum number of edges which must traverse the handle in a toroidal embedding of a graph. After defining the characteristic, flat polygon projections are used to explore efficient toroidal embeddings. Using this exploration we then show an upper bound for the handle number of toroidal graphs. Finally, we prove an inequality between the handle number and graph skewness and conjecture...
