Besides the well known Wiener index, which sums up the distances between allthe pairs of vertices, and the hyper-Wiener index, which includes also thesquares of distances, the edge versions of both indices attracted a lot ofattention in the recent years. In this paper we consider the edge-Wiener index and the edge-hyper-Wienerindex of phenylenes, which represent an important class of molecular graphs.For an arbitrary phenylene, four quotient trees based on the elementary cutsare defined in a similar way as it was previously done for benzenoid systems.The computation of the edge-Wiener index of the phenylene is then reduced tothe calculation of the weighted Wiener indices of the corresponding quotienttrees. Furthermore, a method for computing the edge-hyper-Wiener index ofphenylenes is described. Finally, the application of these results gives closedformulas for the edge-Wiener index and the edge-hyper-Wiener index of linearphenylenes.
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