Abstract. Wiener index is the sum of all distances in a graph. Line graph operator creates a new graph from the old one in such a way that the edges of the old graph are the vertices of the new one, and new vertices are adjacent whenever the corresponding edges were adjacent in the original graph. Repeating the line graph operator we obtain iterated line graphs.

In this chapter we survey known results about the Wiener index with respect to the line graph operator. We also present several conjectures and open problems.