Term for the tree of all paths starting from a given vertex in a graph What is the term for the tree (or a part of the tree) of all possible paths in a graph that start from a given (source) vertex?

This is the tree that is implicitly or explicitly constructed when doing shortest path search.  It appears, for example, in a lecture on search of an MIT Artificial Intelligence course, but I didn't understand if it has a name.

This is not a search tree and not really a decision tree.

Mathematically, it is a covering tree, but is there a more appropriate term in the context of shortest path search?
It's the self-avoiding walk tree (SAW tree).

The trees seem to have been first considered by C.D.&nbsp;Godsil (Matchings and Walks in Graphs, Journal of Graph Theory 5(3):285&ndash;297, 1981; DOI link; just before Lemma&nbsp;2.4), though Godsil doesn't use the name.

(And, yes, "self-avoiding walk" is just a mighty-long way of saying "path".)