Given the following graph:

Graph G:

List all vertices.

List all pairs of adjacent vertices $($edges$).$

Identify a simple path from vertex A to vertex E $.$

Identify a path that is not simple from vertex A to vertex E that.

Identify a cycle within the graph.

Is the given graph connected? Justify your answer.

Is the given graph complete? Justify your answer.

Draw a subgraph of the given graph that includes vertices $\{A,B,C\}$ and all edges between them.

If you were to add an edge between every pair of vertices, what type of graph would you get? Draw this graph.

Convert the given graph into a directed graph by assigning a direction to each edge. Draw the directed graph.

Assign a weight to each edge and redraw the graph as a weighted graph. Provide a sample weight for each

edge.

Remove one vertex in such a way to make the graph disconnected.