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Dec 20, 2016 at 15:15 comment added Mohammad Al-Turkistany @monkeymaths Yes, another variant is restricting A to contain only distances greater than 2.
Dec 20, 2016 at 14:44 comment added monkeymaths A more interesting question can be obtained if $A$ is not bound to contain distances between ALL pairs of vertices, but just between the vertices in some subset of $V(G)$.
Dec 20, 2016 at 14:11 vote accept Mohammad Al-Turkistany
Dec 20, 2016 at 13:57 answer added Tony Huynh timeline score: 3
Dec 20, 2016 at 13:50 history edited Mohammad Al-Turkistany CC BY-SA 3.0
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Dec 20, 2016 at 13:41 comment added Tony Huynh Note that $uv$ is an edge of $G$ if and only if the distance between $u$ and $v$ is $1$. Thus, you know all the edges, and hence the entire graph (in polynomial-time).
Dec 20, 2016 at 13:30 history asked Mohammad Al-Turkistany CC BY-SA 3.0