A difference vertex labeling of a graph G an assignment f of labels to the vertex of G that induces for each edge xy the weight | f(x) - f(y)|. A difference vertex labeling f of a graph G of size n is odd-graceful if f is an injection from V(G) to {0, 1, 2, …, 2q-1} such that the induced weights are {1, 3, 5, …, 2q-1}. In this paper, we generalize Gnanajothi's result on path Pn by showing that the graphs obtained by joining m pendant edges to each vertex of Pn are odd graceful.