Consider the weighted undirected graph with vertices V $=\{$a$,$b$,$c$,$d$,$e$\}$ and the following weighted edges: edge $\{$a$,$b$\}\{$a$,$c$\}\{$a$,$d$\}\{$b$,$d$\}\{$c$,$d$\}\{$c$,$e$\}\{$d$,$e$\}$ weight $8\mathrm{.}04\mathrm{.}07\mathrm{.}02\mathrm{.}02\mathrm{.}11\mathrm{.}03\mathrm{.}0$ Use Prim$$s algorithm from the textbook for finding the minimum spanning tree to answer the following questions. Note, the initial spanning tree is the smallest weight edge with the connecting vertices. Part a: Draw the graph $($please show graph$)$ Part b: Show the spanning tree after the first iteration $($two edges and the connecting vertices$).$ Part c: Show the spanning tree after the second iteration $($three edges and the connecting vertices$).$ Part d: What is the total weight of the edges of the minimum spanning tree produced by the algorithm?

Question $8$

Consider the weighted undirected graph with vertices V$=\{$a$,$b$,$c$,$d$,$e$,$f$\}$ and the following weighted

edges:

Use the version of Dijkstra's algorithm presented in class and in the class slides to find the cost of

the least cost paths with the special $($starting$)$ vertex a$.$ After initialization, the distinguished set is

S$=\{\}$ and the vertex labels are:

Part a: Draw the graph. $($please show graph!!$)$

Part b: What does the set of distinguished vertices S and the list of vertex labels L$($v$)$ look like after

the first iteration of the algorithm?

Part c: What does the set of distinguished vertices S and the list of vertex labels L$($v$)$ look like after

the second iteration of the algorithm?