Please provide all required details, have a clear solution to be graded and upload a PDF of your in Canvas.

$1.$ Given the following graph:

Answer the folunvi$$is $.$

$1\mathrm{.}1$ What type of graph is it$?$

Weighted, directed graph $($can add that it has cycles in it$),$ DAG?

$1\mathrm{.}2$ Provide an adjacency matrix for the graph $($you can use a maximum value $\backslash (\backslash$infty $\backslash )$ to show no relation and the actual cost for a relation$).$

$1\mathrm{.}3$ Provide adjacency lists representation for the graph.

$1\mathrm{.}4$ Dijkstra's algorithm: Find the route with minimum cost from location A to all other locations in the graph using Dijkstra's algorithm. Provide a trace of the algorithm along with the final table similar to example discussed in class slides.

$1\mathrm{.}5$ Can you provide a topological ordering on the graph above? Why or why not?

$2.$ Given the following graph:

$2\mathrm{.}1$ Trace the execution of Prim's algorithm to find the minimum spanning tree for the graph.

$2\mathrm{.}2$ Give the final minimum spanning tree.