$7\mathrm{.}2$ Problem $7$

Problem $7.$ Consider the weighted graph $G(V,E,w)$ below of the neighbouring cities around Boulder, Colorado. Clearly list the order in which Kruskal's algorithm adds edges to a minimum$-$weight spanning tree for $G.$ Clearly, illustrate the final MST using LaTeX $($Note: Reuse the code given below$).$ Additionally, articulate the steps that Kruskal's algorithm takes as it selects the first four edges.

Proof.