data structures using in the algorithmwe use priority queue in which edges that have minimum weight takes priority over any other edge in the graph when the kruskal' algorithm terminatesthe forest has only one component and forms minimum spanning tree of the graph the running time of kruskal' algorithm can be given as ( log )where is the number of edges and is the number of vertices in the graph example apply kruskal' algorithm on the graph given in fig initiallywe have {{ }{ }{ }{ }{ }{ }mst { {(ad)(ef)(ce)(ed)(cd)(df)(ac)(ab)(bc)step remove the edge (adfrom and make the following changesfigure {{ad}{ }{ }{ }{ }mst {adq {(ef)(ce)(ed)(cd)(df)(ac)(ab)(bc) step remove the edge (effrom and make the following changesa {{ad}{ }{ }{ef}mst {(ad)(ef) {(ce)(ed)(cd)(df)(ac)(ab)(bc) step remove the edge (cefrom and make the following changesa {{ad}{ }{cef}mst {(ad)(ce)(ef) {(ed)(cd)(df)(ac)(ab)(bc) step remove the edge (edfrom and make the following changesa {{acdef}{ }mst {(ad)(ce)(ef)(ed) {(cd)(df)(ac)(ab)(bc) step remove the edge (cdfrom note that this edge does not connect different treesso simply discard this edge only an edge connecting (adcefto will be added to the mst therefore