Antimagic labeling conjecture for subdivided caterpillars

Let $T$ be a caterpillar, and let $G$ be a subdivided caterpillar, meaning a subdivision of $T$ in which all edges of $T$ that are not on the central path of $T$ are subdivided the same number of times. An antimagic labeling of $G$ is a bijection $\tau:E(G)\rightarrow \{1,2,\ldots,|E(G)|\}$ such that the sums of labels on edges incident with distinct vertices are different. Subdivided-caterpillar antimagic labeling conjecture. Every subdivided caterpillar is antimagic. The paper proves that every subdivided caterpillar admits an antimagic orientation, and notes that the undirected antimagic-labeling assertion remains an open problem.