Given a connected, undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together. A single graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree.
(BQ) Part 2 book "Algorithms" has contents: Undirected graphs, directed graphs, minimum spanning trees, shortest paths, string sorts, substring search, regular expressions, data compression, tries,... and other contents.
The definition of a tree accepted by science and the forestry industry
is “A woody plant (arboreal perennial) usually with a single columnar
stem capable of reaching six metres in height”. Less than six metres
(21ft) of potential height is regarded as a shrub.This definition is not absolute; gardeners
contest the height threshold, some
preferring five metres (17ft) and others
choosing a threshold of three metres
(13ft). It is likely that bonsai enthusiasts
would entirely dismiss any figures
Lecture Discrete mathematics and its applications (7/e) – Chapter 11: Trees. This chapter presents the following content: Introduction to trees, applications of trees, tree traversal, spanning trees, minimum spanning trees.
(BQ) Part 1 book "Algorithms" has contents: Algorithms with numbers, Divide-and-conquer algorithms, decompositions of graphs, paths in graphs, greedy algorithms, minimum spanning trees, pinimum spanning trees, shortest paths in the presence of negative edges,... and other contents.
The uniform spanning forest (USF) in Zd is the weak limit of random, uniformly chosen, spanning trees in [−n, n]d . Pemantle  proved that the USF consists a.s. of a single tree if and only if d ≤ 4. We prove that any two components of the USF in Zd are adjacent a.s. if 5 ≤ d ≤ 8, but not if d ≥ 9. More generally, let N (x, y) be the minimum number of edges outside the USF in a path joining x and y in Zd . Then max N (x, y) : x, y ∈ Zd = (d − 1)/4 a.s.
(BQ) Part 1 book "Introduction to algorithms" has contents: Data structures for disjoint sets, elementary graph algorithms, minimum spanning trees, single source shortest paths, maximum flow, multithreaded algorithms, matrix operations,...and other contents.