Tree spanner

in which the distance between every pair of vertices is at most

There are several papers written on the subject of tree spanners.

One of these was entitled Tree Spanners[1] written by mathematicians Leizhen Cai and Derek Corneil, which explored theoretical and algorithmic problems associated with tree spanners.

Some of the conclusions from that paper are listed below.

is always the number of vertices of the graph, and

The lowest tree spanner for the graph is because of the necessarily longer path between vertices 2 and 3, which is times as long as the shortest distance between them in