How many regions does the following planar graph have?

Select one:$543$The graph is not planar$\mathrm{.}6$

Let $\backslash ($ G $\backslash )$ be a weighted complete graph with at least $3$ vertices. Suppose $\backslash ($ G $\backslash )$ has two distinct vertices labelled $\backslash ($ X $\backslash )$ and $\backslash ($ Y $\backslash ).$ Suppose we know the following facts about $\backslash ($ G $\backslash ).$

$($a$)$ The Nearest Neighbour Heuristic returns the output $13,$ when starting at vertex $\backslash ($ X $\backslash ).$

$($b$)$ The Nearest Neighbour Heuristic returns the output $16,$ when starting at vertex $\backslash ($ Y $\backslash ).$

Inoindent Which of the statements below concerning the optimal solution to a Travelling Salesman Problem on $\backslash ($ G $\backslash )$ may be deduced from the above facts?

Select one:The optimal solution is at most $16.$The optimal solution is at most $13.$The optimal solution lies between $13$ and $16.$The optimal solution is equal to $13.$The optimal solution is equal to $16.$