Please, answer all parts of the question with a clear graph representation and explain all the following steps.

Question 1.

Let there is an undirected graph with 10 nodes with the following edges (x-y means x and y are connected):

1-4, 1-2, 2-3, 2-8, 2-5, 2-7, 3-9, 3-10, 4-3, 5-6, 5-7, 5-8, 8-7. Now,

1. Express these relations as a graph.
2. Apply BFS considering 1 as the source node (level-0 node). Draw the BFS tree and mark each level. If there are multiple options at any step, pick the node with smaller index.
3. Repeat part II considering six as the source node (level-0 node).

Question 2.

Consider the same graph mentioned in Question 1. Now,

1. Apply DFS considering 1 as the source node. If there are multiple options at any step, pick the node with smaller index. Draw the DFS tree. Also, mention all the back-edges.
2. Repeat part II considering 6 as the source node.