A/ Consider the following graph, find the Maximal Flow from source vertex s to sink vertex d, by using (Max-flow Min-Cut Theorem). S 2. a C -3-b 2- d

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A: Yes, it's possible to design a polynomial time algorithm to meet all demands and supplies. Attach a…

Q: What does the GRANT statement imply and how does it apply to safety? Are there any limitations on…

A: The GRANT declaration: The SQL Provide command grants users access to or rights over database…

Q: (c) You are given a directed graph G where all edge weights are positive. Given two vertices s and t…

A: Оne  аlgоrithm  fоr  finding  the  shоrtest  раth  frоm  а  stаrting  nоde  tо  а  tаrget  nоde  in…

Q: Run Dijkstra's algorithm on the weighted graph below, starting at vertex A. Show every step in the…

A: In the below figure gave  step step explanation.

Q: Let G be a directed graph with positive and negative weights. It is known that the shortest paths…

A: The algorithm is Bellman- ford.Time complexity is O(ne ),Where n is number of node ,e is number of…

Q: Part 2: Random Graphs A tournament T is a complete graph whose edges are all oriented. Given a…

A: Answer is given below-

Q: B 2 A 6 2 7 6 10 D E F 10 1 12 G

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Q: = Let G (V, E) be a directed graph. Suppose we have performed a DFS traversal of G, and for each…

A: Proofs for a, b is given below :

Q: Problem 3: Consider the following weighted graph: 5 1. Find the length of the shortest path between…

A: We need to find the shortest lenght path between a and z.We can apply the dijkstra's technique.

Q: The graph below does not have an Euler path and does not have an Euler circuit.

A: a)  Euler Path: A path that travels every edge of a connected graph once and only once and starts…

Q: 1. Let F be a forest with n vertices and k connected components, with 1 < k <n. (a) Compute ) deg(v)…

A: Answer:  I have given answer in the handwritten format.

Q: 6. Use a depth first search starting at vertex a to find a spanning tree for the given graph.

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Q: 1. Consider the following directed graph. A C F J D G В E H I 1. What are the sources and sinks of…

A: According to the information given:- We have to follow the graph and find the source and sink , one…

Q: Problem 3: For each of the two graphs below, determine whether they are planar. Justify your answer:…

A: In graph theory, a planar graph is a graph that can be embedded in the plane, using the kuratowski's…

Q: Question 7 Here, 0-2(1) means 2 is reachable from 0 at a cost of 1. Find all pair shortest path…

A:

Q: Dijkstra's algorithm

A: Given :- A directed graph along with the weights is mentioned in the above  question

Q: Find the all-pair shortest path for the following graph.

A: Summary:In this question, we need to find all pairs of shortest paths for the given graph.

Q: Problem B5: Let G be the directed graph below: I Use matrix multiplication to compute the number of…

A: Given a directed graph G consisting of four nodes : 2,3,4,1 . The above graph is directed because it…

Q: Let G be a directed graph with positive and negative weights. You are given that the shortest paths…

A: For finding all the shortest path from s we can use the bellman-ford algorithm to do that.  The…

Q: Which of the following problems can be solved in O(n3) time, where n is the number of vertices in…

A: The objective of the question is to identify which of the given problems can be solved in O(n^3)…

Q: Model the following problem as a network flow problem and write down the corresponding linear…

A: first we have to formulate given graph in matrix form       [0, 1, 1, 0, 0]  [0, 0, 1, 0, 1]  [0,…

Q: 16. Use the flow graph of K; to answer the following questions. a 6/6 9/11 3/4 6/6 3/3 3/3 2/2 8/8…

A: The answer to all the parts along with their explanation is given below:

Q: Consider the following graph: 2 5 6 4 NI 2 E /10 H 5 F Find the shortest path from node C to all the…

A: Here, we are going to find the single source shortest path for Node C using Dijkstra's algorithm.…

Q: Use graph theory: Let G be a directly acyclic graph with at least two vertices. Suppose we add a…

A: Dear Student, We can use graph theory to prove that a directly acyclic graph G with at least two…

Q: Given a graph that is a tree (connected and acyclic).   (I) Pick any vertex v. (II) Compute the…

A: Given a graph that is a tree (connected and acyclic).   We have to explain which option is true for…

Q: Give the depth-first traversal of the following graph beginning at vertex A. F B A D E

A: An algorithm for navigating or searching through tree or graph data structures is called depth-first…

Q: Problem 1. In Fig. 1 there is a weighted graph, circles represent vertices, links represent edges,…

A:

Q: Consider the following graph G Determine whether the following graph G is bipartite. If so, color…

A: Bipartite graph :   A graph G=(V, E) is called a bipartite graph if its vertices V can be…

Q: Use the matrix tree theorem to find the number of spanning trees in the complete graph on 4 nodes…

A: I have handwritten the solution, Please appreciate: Solution:

Q: Let n be an even positive integer. (a) Show that if the degree of every vertex in a simple graph G…

A: Given that, n is an even positive integer. (a) Consider an example of the graph with, n=4 then the…

Q: 5. Consider the following graph G (a) How many paths of length 5 are there between vertices 1 and 2?…

A: Hey there, I am writing the required solution based on the above given question. Please do find the…

Q: BFS and its applications: You are given a directed graph G = (V, E), %3D and a special vertex v.…

A: BFS means Breadth first Search, It traverse the graph level by level and For BFS traversal Queue…

Q: Consider the following undirected graph. b s (a) How many edges are there in this graph? (b) Give…

A: (a) The given graph contains the following edges: a self-loop on vertex a (a-b) (a-e) (b-c) (b-d)…

Q: You are given a simple connected undirected graph with N nodes(or vertices) for computing a Minimum…

A: Minimum Spanning Tree of a connected undirected graph is a subset of edges of that graph that…

Q: Let G be the following directed graph. e1 Is the function / onto? O Yes Ο NO Why or why not? es I eg…

A: In the following directed graph, V is the set of vertices in G and E is the set of edges in G. The…

Q: Using Floyd's algorithm, compute the distance matrix for the weight directed graph defined by the…

A:

Q: Consider an undirected graph with 100 nodes. Give the maximum number of edges the graph can contain…

A: We are given an undirected graph with 100 nodes and we are asked the maximum number of edges in a…

Q: do you notice? The sum of the indegrees equals the sum of the outdegrees. The sum of the outdegrees…

A: Solution - In the given question, we have to select the correct answer from the given options.

Q: True or False    Let (u, v) be an edge in a maximum flow graph with capacity greater than 0. Then…

A: Given: Is it true or false? In a maximum flow graph with capacity larger than 0, let (u, v) be an…

Q: (a) Draw the corresponding graph. (b) Write down the adjacency matrix A for this graph. Calculate…

A: Given adjacency list is: 1 2, 3, 4 2 1 3 1, 4 4 1, 3 5 -

Q: 5. Show the adjacency matrix for this graph, where vertex i is represented by the i-th row and i-th…

A: The adjacency matrix for a graph can be made by following rules. 1. Put 1 if there is a direct edge…

Q: 1. Consider the weighted, directed graph containing the following vertices and edges. (Weights are…

A: 1. Consider the weighted, directed graph containing the following vertices and edges.(Weights are in…

Q: 2. Consider the graph given by the following adjacency list: vertex adjacent vertics 1 2, 3, 4 2…

A: Given adjacency list is: 1 2, 3, 4 2 1 3 1, 4 4 1, 3 5 -