I believe I know the answer but I wanted a clarification on the definition of $d_k$, because it is said to be defined as 

"the shortest distance from vertex i to vertex j in the graph obtained by removing the edge to be repaired on day k from the original graph"

But I believe it should be stated as 

"the shortest distance from vertex i to vertex j in the graph obtained by removing the edgeS to be repaired on day k from the original graph" (notice the plural on edges with the uppercase S).

I believe this is the case because otherwise we would be imposing only one removal per day, which contradicts the problem statement, and also would make no sense to define the distance when there is no connection between two points, since the graph is guaranteed to be connected if only one edge is removed. 

I do not think this superfluous detail changes much, but I noticed it and I think it would improve the statement just a little bit (I think it was pretty clear though).

Thank you for pointing out the mistake.
"edges" is correct, not "edge".

Announcement

We revised the explanation of the edge weights in the problem statement because it was not clear.
Edge weight represents the distance it takes to move on that edge.

問題文中の辺の重みの説明が分かりにくかったため修正しました。
辺の重みはその辺上を移動するのにかかる移動距離を表します。