Before revision:  For a source vertex set S\subseteq V in a digraph G(V,E), an S-source-wise round-trip spanner of G of stretch k is a subgraph H of G such that for every u\in S ,v\in V, the round-trip distance between u and v in H is at most k times of the original distance in G. We show that , for a digraph G(V,E)
After revision:  For a source vertex set S\subseteq V in a digraph G(V,E), an S-source-wise round-trip spanner of G of stretch k is a subgraph H of G such that for every u\in S ,v\in V, the round-trip distance in H is at most k times of the original distance in G. We show that , for a digraph G(V,E)