Q$1.$ Jodhpur Development Authority is responsible for following network of roads. The JDA office is based at $A.$

$($a$)$ A JDA supervisor has to inspect all the roads, starting and finishing at $A.$ Find the length of an optimal route using CPP$.$

$($b$)$ An engineer working at A has his residence at H$.$ He also wishes to inspect all the roads. He wishes to start his route at A and finish at $H.$ Utilize CPP to determine the length of an optimal route for the engineer.

Q$2.$ Is it possible to have a cycle graph which is isomorphic to its complement? If yes, please provide the both the graph and prove that they are isomorphic. If not, why?

Q$3.$ Let $G=(V,E)$ be an undirected graph such that $V=xY$ and $xY=.$ Then prove that ${\displaystyle \underset{\text{x}\text{i}\text{n}\text{x}}{\overset{?}{}}}$deg$(x)={\displaystyle \underset{\text{y}\text{i}\text{n}\text{Y}}{\overset{?}{}}}$deg$(y).$

Q$4.$ Find the