Caterpillars are Antimagic

An antimagic labeling of a graph G is bijection from the set edges E(G) to $$\{1,2,\ldots ,|E(G)|\}$$ , such that all vertex sums are pairwise distinct, where sum at u labels assigned incident u. A called when it has an labeling. Hartsfield and Ringel conjectured every simple connected other than $$K_2$$ conjecture remains open even for trees. Here, we prove caterpillars by means $$O(n \log n)$$ algorithm.