f possible, draw an example of each graph as described. Otherwise, describe why such a graph

does not exist. Unless otherwise specified, each graph is undirected and has exactly $6$ nodes.

Please use uppercase letters starting at A to index the nodes of your graph.

Remember, a simple path is a sequence of unique, adjacent edges.

For this problem you can embed photographs of neatly drawn graphs into your HW document.

$($a$)[2$ pts$.]$ A graph where every node has degree $3.$

$($b$)[2$ pts$.]$ An acyclic graph with a node with degree $2$ and a different node with degree $5.$

$($c$)[2$ pts$.]$ A rooted tree of height $3$ with $3$ leaves. Note that leaves are nodes with no children

and the height of a tree is the lenth of the longest path from the root to a leaf.

$($d$)[2$ pts$.]$ A weighted graph that is a tree with a simple path of weight $4$ from A to D$,$ a simple

path of weight $2$ from A to F$,$ a simple path of weight $6$ from D to F$,$ and no edges shared by

any two of A$,$ D$,$ and F$.$

$($e$)[2$ pts$.]$ A strongly connected, directed graph with exactly $7$ edges