Discrete Mathematics:

Consider the following graph:

$($a$)$ Run Kruskal's minimum spanning tree algorithm on the graph. Use the following table with three columns to represent your answers. The first column is the step number. The second column is the edge chosen. The third column is the weight of the edge chosen. You are required to use the following table as the template.

Step

$...$

$...$

Edge

$...$

Weight

$...$

$...$

$($b$)$ Run Prim's minimum spanning tree algorithm on the same graph. Use the following table with three columns to represent your answers. The first column is the step number. The second column is the edge chosen. The third column is the weight of the edge chosen. You are required to use the following table as the template.

Step

$...$

$...$

Weight

$...$

$...$

$($c$)$ Run Dijkstra's algorithm on the same graph to compute the shortest path from a to f $,$ using the following table as the template. The first column is the step number. The second column is the edge chosen. The third column is the vertex chosen. The fourth column is the weight of the shortest path from the starting vertex to the chosen vertex.

Furthermore, write down the shortest path you obtain AND its weight.

Step

$...$

$...$

Edge

$...$

Vertex

$...$

Path Weight