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I'm looking at a specific type of graph, and my google-fu has failed me. The graph $G$ is a connected unweighted directed graph where for each pair of vertices $(u,v) \in G$ the shortest path from $u$ to $v$ is unique.

What is such a graph called?

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Geodetic? cstheory.stackexchange.com/questions/16354/… answers this question anyhow! –  Sharkos May 8 '13 at 15:38

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up vote 2 down vote accepted

Yes, such graphs are apparently referred to as geodetic graphs, as in http://www.graphclasses.org/classes/gc_96.html My first guess was geodesic, so I wasn't far off.

Elsewhere on the internet, USP seems to be used as an obvious acronym.

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Perfect, thanks! –  Foo Barrigno May 8 '13 at 16:17

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