Assertion: graph's vertex | /r/CapableOf | lie on a shortest path
Facets:
value: for all a
type: TRANSITIVE-OBJECT
Source sentences:
text: Conversely, if a median graph G contains two vertices 0 and 1 such that every other vertex lies on a shortest path between the two (equivalently, m(0,a,1) = a for all a), then we may define a distributive lattice in which a ∧ b = m(a,0,b) and a ∨ b = m(a,1,b), and G will be the graph of this lattice.
text: In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest paths between each pair of a, b, and c.