Abstract
Solairaju and Chithra introduced a new type of labeling of a graph G with p vertices and q edges called an edge odd graceful labeling if there is a bijection f from the edges of the graph to the set \{1,3,\ldots,2q-1\} such that, when each vertex is assigned the sum of all edges incident to it \bmod ~ 2q , the resulting vertex labels are distinct. In this paper, we proved necessary and sufficient conditions for the cylinder grid graph C_{m,n} = P_{m} \times C_{n} and torus grid graph T_{m,n} =C_{m} \times C_{n} are edge odd graceful.