a) Given a depth-first search tree T, the set of edges in T are referred to as "tree edges" while those not in T are referred to as "back edges". Modify the implementation of the Depth-First Search algorithm to print out the set of tree edges and the set of back edges for the following graph. 1(0 1 1 0 0 1 0) 210 100 0 0 31 10 10 1 4 0 0 1 0 0 0 0 50 0 0 00 1 1 1 0 1 70 0 1 0 1 1 0 6 1 0 0 0

4. Please apply Kruskal's spanning tree algorithm in the graph below and find the minimum spanning tree (MST). Edge weights are in the adjacency matrix table. (you can list the edges in MST or draw the tree below) d b a e h f The adjacency matrix for the undirected weighted graph is mentioned below: a d e g h a 4 8 4 8 11 8. 7 4 2 d 7 14 e 9. 10 f 4 14 10 2 1 6. 8. 11 1 7 7

If I pick a vertex on Luna's graph (pictured, Question 1), at random, and run Prim's Algorithm, let X be the number of edges in the minimum spanning tree that results. What is E[X] + 14?

Draw a tree with 14 vertices Draw a directed acyclic graph with 6 vertices and 14 edges Suppose that your computer only has enough memory to store 40000 entries. Which best graph data structure(s) – you can choose more than 1 -- should you use to store a simple undirected graph with 200 vertices, 19900 edges, and the existence of edge(u,v) is frequently asked? - Adjacency Matrix - Adjacency List - Edge List

If I pick a vertex on the graph, at random, and run Prim's Algorithm, let X be the number of edges in the minimum spanning tree that results. What is E[X] + 14?

5. Fleury's algorithm is an optimisation solution for finding a Euler Circuit of Euler Path in a graph, if they exist. Describe how this algorithm will always find a path or circuit if it exists. Describe how you calculate if the graph is connected at each edge removal. Fleury's Algorithm: The algorithm starts at a vertex of v odd degree, or, if the graph has none, it starts with an arbitrarily chosen vertex. At each step it chooses the next edge in the path to be one whose deletion would not disconnect the graph, unless there is no such edge, in which case it picks the remaining edge (a bridge) left at the current vertex. It then moves to the other endpoint of that edge and adds the edge to the path or circuit. At the end of the algorithm there are no edges left ( or all your bridges are burnt). (NOTE: Please elaborate on the answer and explain. Please do not copy-paste the answer from the internet or from Chegg.)

The following table presents the implementation of Dijkstra's algorithm on the evaluated graph G with 8 vertices. a) What do the marks (0, {a}) and (∞, {x}) in the 1st row of the table mean? b) What do the marks marked in blue in the table mean? c) Reconstruct all edges of the graph G resulting from the first 5 rows of the table of Dijkstra's algorithm. d) How many different shortest paths exist in the graph G between the vertices a and g?

For the following graph, list the vertices in the order they might be encountered in a breadth first search (BFS) starting at vertex A. No need to use any spaces, e.g., ACFGHIDBE In cases when there are multiple possibilities for the next vertex, choose them in alphabetical order (for reference: A, B, C, D, E, F, G, H, I) A B E H

Q: Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a weighted graph. Given a graph and a source vertex in the graph, find shortest paths from source vertex (E) to all vertices in the graph below.