Problem $4.(40\%)$ Consider a weighted graph $G=(V,E)$ with $5$ vertices defined with

$V=\{1,2,3,4,5\},E=\{(1,2),(2,3),(4,5),(1,3),(2,4),(3,5),(2,5)\}$

where the weights are given by $w(i,j)=|i-j{|}^2$ for any $(i,j)inVV.$

$($a$)(5\%)$ Draw the graph, and label the weights of each edge on the graph.

$($b$)(25\%)$ Apply Dijkstra's algorithm to find a shortest path from vertex $\text{'}1\text{'}$ to vertex $\text{'}5\text{'}.$ What is the length of shortest path?

$($c$)(10\%)$ Is the shortest path you found in part $($b$)$ unique? List all the shortest path for this graph.