In 1991 Gnanajothi conjectured: Each tree is odd-graceful. In this paper, we define the edge-ordered odd-graceful labeling of trees and show the odd-gracefulness of all symmetric trees.
Xianggian Zhou, Bing Yao, Ming Yao , Xiang’en Chen. On Odd-gracefulness of All Symmetric Trees[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 087. 309-319. .