Use the minimum cut algorithm to find the maximum flow of graph K₁ and find how many different cuts there are in the graph. S O a O Oc Od 4 5 b6 с K₁ d 5 5 7 minimum cuts and the maximum flow is 10 8 minimum cuts and the maximum flow is 13 8 minimum cuts and the maximum flow is 10 9 minimum cuts and the maximum flow is 13

Question 5: Consider the following graph. Find the shortest path from 'a' to all other vertices using Dijkstra's algorithm. Draw graph diagrams to show all intermediate steps. (. 1 4 3 4 a i 3 с 1 2 d 80 g 3

Given the below graph, show the minimum spanning tree using an adjacency matrix. You may use scratch paper to draw the graph if you wish. 12 A В 2 3 E F 8 G H 10 A В D E F G A В C D E F G H |||

Given a graph G, please do the following: a) Show the adjacency matrix for graph G. b) Show the adjacency list for graph G. I 1 6 2 4 7 3 5 Graph G

Consider the directed graph shown below. Which of the following statements are true? b a e d 9 The shortest path from "a" to "g" is of length 3. The shortest path from "a" to "g" is of length 4. The shortest path from "a" to "g" is of length 5. The in-degree of "a" is 1. The in-degree of "a" is 2. O The out-degree of "c" is 1. O The out-degree of "c" is 2. The out-degree of "c" is 3. The graph is acyclic. The ordering "a,b,c,d,e,f,g" is a topological sort for the graph. The ordering "c,b,a,d,f,e,g" is a topological sort for the graph. The graph has 1 strongly connected component. The graph has 2 strongly connected components. The graph has 3 strongly connected components.

Based on the undirected Graph G: e₁ es e10 V₁ es e6 e10 V4 e6 e3 V4 e9 e11 e3 eg e7 e11 e₂ e7 V₂ Undirected Graph G a) Find the degree of each vertex in the undirected Graph G. b) Find the adjacency matrix and incidence matrix of Graph G. c) If undirected Graph G is converted into a directed Graph G as in Figure 2, find the in- degree and out-degree for each vertices. e₁ es V5 e12 e2 V₂ es V5 e4 e12 e13 e4 e13. V3 Figure 2: Directed Graph G e14 V3 e14

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V4 Draw the complement of the graph:

Run the Bellman-Ford algorithm for the following graph starting from the node a 3 b a 7 d G

Compute the maximum flow in the following flow network using Ford-Fulkerson's algorithm. 12 8 14 15 11 2 5 1 3 d 7 f 6 What is the maximum flow value? A minimum cut has exactly which vertices on one side? 4.