$($e$)\backslash ($ G$\_\{1\}\backslash )$ is not a connected graph. If you wanted to turn $\backslash ($ G$\_\{1\}\backslash )$ into a connected graph by adding edges, how many would you need to add? Which edges would you add?

Note: There are many possible answers to this question. If you say you only need $3$ edges, then your answer should consist of just $3$ edges. If you say you only need $1$ edge, your answer should consist of just $1$ edge.

$($f$)$ A connected component in a graph is a maximal set of vertices that are all connected to each other. $($Here$,$ "maximal" means that if you add any more vertices, it won't be connected anymore.$)$

What are the vertices in the connected component that contains $4?$

$($g$)$ How many connected components does $\backslash ($ G$\_\{1\}\backslash )$ have?

$($h$)$ If a graph is connected, what does that tell you about how many connected components it has?

$($i$)$ How many edges are there in the longest possible path in $\backslash ($ G$\_\{1\}\backslash )?$

$($j$)$ How many edges are there in the longest possible trail in $\backslash ($ G$\_\{1\}\backslash )?$

$($k$)$ How many edges are there in the longest possible walk in $\backslash ($ G$\_\{1\}\backslash )?$

$($l$)$ How many edges are there in the longest possible cycle in $\backslash ($ G$\_\{1\}\backslash )?$