Answer each question for the graph shown below.

You can answer most of the questions by drawing a copy of the graph and then "coloring",

"shading" or in some other way "marking" the graph to show you answers. Any justifications

required should be brief and relate to the particular graph shown belos:

Part $1$:

Draw a DFS tree with backedges for the given graph.

Draw a BFS tree with crossedges for the given graph.

Part $2$:

Does this graph have a Hamiltonian Circuit? If so$,$ list the circuit in the order of the

vertices. If not, demonstrate why there cannot be a Hamiltonian Circuit.

Does this graph have a Hamiltonian Path. If so$,$ list the path in the order of the vertices.

If not, demonstrate why there connot be a Hamiltonian Path.

What is the minimum number of colors needed to color the vertices so that no two

adjacent vertices are the same color? Demonstrate your coloring!

What is the minimum number od colors needed to color the edges so that no two adjacent

edges are the same color. Demonstrate your coloring!

A clique is a complete subgraph of a graph. $($Complete means there is an edge between

every pair of vertices.$)$ Identify cliques in the above graph, and give the number of

vertices in the maximal clique.Answer each question for the molecules shown. Does the molecule shown below have a geometric isomer? Are the following compounds constitutional isomers?