A labeling of a graph $G$ with $\alpha$ vertices and $\beta$ edges is called an edge odd graceful labeling if there is an edge labeling with odd numbers to all edges such that each vertex is assigned a label which is the sum $\mod (2\gamma)$ of labels of edge incident on it, where $\gamma=max\{\alpha,\beta\}$ and the induced vertex labels are distinct.

Keywords: Graceful labeling, edge odd graceful labeling.