Abstract. Let G be a graph. Denote by Lⁱ(G) its i-iterated line graph and denote by W(G) its Wiener index. Dobrynin, Entringer and Gutman formulated a problem of characterizing all nontrivial trees T and i≥3, such that W(Lⁱ(T))=W(T).

In a series of papers we completely solve this problem. This is 3rd paper of the series and we prove here that there is no tree T homeomorphic to the claw K_1,3 and i≥4 such that W(Lⁱ(T))=W(T).