a spanning tree, but has weights or lengths associated with the edges, and the total weight of the tree (the sum of the weights of its edges) is at a minimum

a spanning tree T such that is minimal

a tree containing each vertex in the graph such that the sum of the edges' weights is minimum

a tree formed from a subset of the edges in a given undirected graph

(n.) a spanning tree with the smallest possible weight among all spanning trees for a given graph.

Minimum Spanning Tree

(MST) A tree in a weighted graph that contains all of the graph's vertices, where the sum of the weights along the edges is minimal.

Given a connected, undirected graph, a spanning tree of that graph is a subgraph which 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.