An antimagic labeling of a graph G is an injection from E(G) to {1,2,…,|E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to edges incident to u. A graph is called antimagic when it has an antimagic labeling. Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic and the conjecture remains open even for trees. Here we prove that caterpillars are antimagic by means of an O(nlogn) alg...
An antimagic labeling of a graph G is an injection from E(G) to {1,2,…,|E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to edges incident to u. A graph is called antimagic when it has an antimagic labeling. Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic and the conjecture remains open even for trees. Here we prove that caterpillars are antimagic by means of an O(nlogn) algorithm.