Problem $5.$ Draw the Graph $(10$ points$)$

If 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.

Solution: