kruskal' algorithm the reason proposition is so important is that it can be used as the basis for building minimum spanning tree in kruskal' algorithmit is used to build the minimum spanning tree in clusters initiallyeach vertex is in its own cluster all by itself the algorithm then considers each edge in turnordered by increasing weight if an edge connects two different clustersthen is added to the set of edges of the minimum spanning treeand the two clusters connected by are merged into single cluster ifon the other hande connects two vertices that are already in the same clusterthen is discarded once the algorithm has added enough edges to form spanning treeit terminates and outputs this tree as the minimum spanning tree we give pseudo-code for kruskal' mst algorithm in code fragment and we show the working of this algorithm in figures and code fragment kruskal' algorithm for the mst problem as mentioned beforethe correctness of kruskal' algorithm follows from the crucial fact about minimum spanning treesproposition each time kruskal' algorithm adds an edge ( ,uto the minimum spanning tree twe can define partitioning of the set of vertices (as in the propositionby letting be the cluster containing and letting contain the rest of the vertices in this clearly defines disjoint partitioning of the vertices of andmore importantlysince we are extracting edges from in order by their weightse must be minimum-weight edge with one vertex in and the other in thuskruskal' algorithm always adds valid minimum spanning tree edge