Minimum Cost Spanning Tree Using Prim's Algorithm

A spanning tree of a graph is just a sub-graph that contains all the vertices and is a tree (with no cycle). A graph may have many spanning trees. If the graph is a weighted graph (length associated with each edge). The weight of the tree is just the sum of weights of its edges. Obviously, different spanning trees have different weights or lengths. Our objective is to find the minimum cost (weight) spanning tree.