9. Use Prim's algorithm to find a minimal spanning tree for the weighted graph in the following figure. Use A as the initial vertex and list the edges in the order in which they are chosen, and give the diagraph of the tree... (7) B 3 D لا 2 3 A F 2 5 4 C E
Q: the minimum spanning tree
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Q: algorithm
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Q: An undirected weighted graph G is given below: 11 3 1 -4.1 2 .2 3. b. a (a) Use Prim's algorithm to…
A: solution of the given question is:-
Q: The number of spanning trees from the following graph are a
A: The answer is given in the steps below.
Q: 1. Use the depth-first algorithm to find a spanning tree.
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A: possible spanning tree:-- in spanning tree their is no cycle is allowed.
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- 10 15 13 4 16 12 14 H Consider the graph given above. Use Kruskal's algorithm to find the minimum spanning tree. a. What is the total weight of the spanning tree? b. List the weights of the selected edges separated by commas in the order of selection.3. Let G be the following graph. V1 V7 V2 V8 V5 V6 V3 V4 (a) Using the greedy algorithm, proper vertex-color G with the order V₁, V2, V3, V4, V5, V6, V7, Vg. How many colors did you use? (b) Find x(G) and show a coloring that demonstrates this. (c) Provide an ordering of the vertices that when input into the greedy algorithm, produces a proper vertex-coloring that uses x(G) many colors.4. Consider the following graph. Apply Kruskal’s algorithm to find the minimum spanning tree and write the sequence of edges added to the tree. E B D A 15 5 I 2 4 3 6 10 5 H 12 TI F
- A) Give the minimum spanning tree using Prim’s algorithm (starting at vertex A). B) Give the minimum spanning tree using Kruskal’s algorithm. C) What is the total weight of the minimum spanning tree?43. Find a Steiner tree of the graph K, with the vertices b, j, d, h by listing the edges that form your Steiner tree. a Ks List the edges that form your Steiner tree here:There are n med-school students and n hospitals. Each med-schoolstudent has a strict preference over the hospitals, and each hospital has a strict preference over themed-school students. Hospitals and students are matched using the Gale-Shapely algorithm. (a) Prove that there is no matching, stable or unstable, in which every hospital has a stu-dent whom it prefers to its student in the stable matching resulted by Gale-Shapely algorithm.(Use contradiction to prove the argument, and consider the last student who receives aproposal in the Gale-Shapely algorithm.) (b) Provide an example in which a student benefits from falsifying their preference list inthe Gale-Shapely Algorithm. (Use the example with three med-school students and threehospitals.)
- Question 3: Find the Minimum Spanning Tree for the given graph using Prim's algorithm and write the steps. A 4 2 11 с F 8 7 1 2 E D 6 B 7 4 2 G H 5 9 10 TQuestion 4: Find the Shortest Path Tree for the given graph using Dijkstra’s algorithm and writeall the steps. The source is from “Home”a) Which edges would you keep for the minimum-weight spanning tree? (Indicate as vertex-vertex — eg. “K-P”... if there were vertices K and P.) b) Describe the algorithm you used to determine the minimum-weight spanning tree above. Did you face any challenges in applying this algorithm?
- Draw the minimum spanning tree for the following graph. Use induction to prove your result is a minimum spanning tree.Please show step-by-step explanations. Thank you. About the Petersen Graph, (a) The Petersen Graph P is shown below. Assign an edge weight of 1 to each edge of P. Use either Kruskal or Prim’s Algorithm to find a (necessarily minimum weight)spanning-tree of P. you must be clear about whichthe algorithm you choose and show and explain each step leading to the spanning tree.6. Determine the breadth-first and depth-first traversals for the following graph: (start with vertex A) B A E