data structures using the running time of prim' algorithm can be given as ( log vwhere is the number of edges and is the number of vertices in the graph figure example construct minimum spanning tree of the graph given in fig graph step choose starting vertex step add the fringe vertices (that are adjacent to athe edges connecting the vertex and fringe vertices are shown with dotted lines step select an edge connecting the tree vertex and the fringe vertex that has the minimum weight and add the selected edge and the vertex to the minimum spanning tree since the edge connecting and has less weightadd to the tree now is not fringe vertex but tree vertex step add the fringe vertices (that are adjacent to cstep select an edge connecting the tree vertex and the fringe vertex that has the minimum weight and add the selected edge and the vertex to the minimum spanning tree since the edge connecting and has less weightadd to the tree now is not fringe vertex but tree vertex step add the fringe vertices (that are adjacent to bstep select an edge connecting the tree vertex and the fringe vertex that has the minimum weight and add the selected edge and the vertex to the minimum spanning tree since the edge connecting and has less weightadd to the tree now is not fringe vertex but tree vertex step notenow node is not connectedso we will add it in the tree because minimum spanning tree is one in which all the nodes are connected with - edges that have minimum weight sothe minimum spanning tree can now be given as step step step step step step step step example construct minimum spanning tree of the graph given in fig start the prim' algorithm from vertex figure graph