. Execute Prim's minimam spanning tree alporithm by hand o the graph below showing how the data strctures evolve specifically indicating when the distance from a fringe vertex to the tree is updated. Clearly indicate which edges become part of the minimum spanning tree and in which order.Start at vertex A 2. Execute Kruskal's algorith on the weighiled tree shown below. Assune thal edges of equal weight will be ia te peiorily q eue ia alpliabetical order. Clearly show whal happens each time an edge is renioved Iron the priority queue and how he dynamic equivalence relation changes on eacla slep and slow the final mini" spanning Ireeat . oivea cxamplo of a weighted graph for which the miaimm spanaing tzee is unique. tudicano wlat the miai spanning troe is for that graph. dive another exanple of a weiglsted graplh that has more thea oso mini spanning tree. shoa wo different minmum spanning trees for that graph. What determines whether a graph has mo ds oe minima speaning teet 4. Given the folloming adjcency lists (with edge weights in parentheses) for a directed graph: A:M3, c(3), D(1)B: CL), D3) Ar6), C(3) E: EIS) F: D3), A4) Exscute Dijkst:a's shonest-path algorithm by hand oa this graph, showiag bow the data stractures evove, withA as the stating vetex. Caly iadicate wlich edges beconw part of the shostest path and ia wich order