Antimagic orientation of subdivided caterpillars

Let m≥1 be an integer and G a graph with m edges. We say that has antimagic orientation if D bijection τ:A(D)→{1,…,m} such no two vertices in have the same vertex-sum under τ, where of vertex v τ is sum labels all arcs entering minus leaving v. Hefetz et al. (2010) conjectured every connected admits orientation. The conjecture was confirmed for certain classes graphs as regular graphs, minimum degree at least 33, bipartite zero or two, trees including caterpillars complete k-ary trees. prove subdivided caterpillar orientation, subdivision T edges are not on central path number times.