A Proof to the Odd-Gracefulness of All Lobsters

Abstract

Gnanajothi conjectured that all trees are odd-graceful and verified this conjecture for all trees with order up to \(10\). Since the
conjecture is open now we present a proof to the odd-gracefulness of all lobsters and show a connection between set-ordered odd-graceful labellings and bipartite graceful labellings in a connected graph.