Question 8. A connected graph G has 4 vertices and 4 edges of costs 1, 2, 3 and respectively 4. (a) Show that G is not a tree. (b) Show that G has a single minimum spanning tree. (Hint: For example, think how Prim's algorithm constructs the minimum spanning tree). (c) Draw a connected graph G with 4 nodes and 4 edges of costs 1, 2, 3, 4, respectively, so that the minimum spanning tree contains the edge of cost 4. The 4 nodes are below, you need to draw the 4 edges and indicate their cost. a b d

Question 8. A connected graph G has 4 vertices and 4 edges of costs 1, 2, 3 and respectively 4. (a) Show that G is not a tree. (b) Show that G has a single minimum spanning tree. (Hint: For example, think how Prim's algorithm constructs the minimum spanning tree). (c) Draw a connected graph G with 4 nodes and 4 edges of costs 1, 2, 3, 4, respectively, so that the minimum spanning tree contains the edge of cost 4. The 4 nodes are below, you need to draw the 4 edges and indicate their cost. a b d

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Q: Answer True or False to the following claims: a. Let G be a connected graph on 42 vertices and G…

A: Given questions are true or false questions so we provide both true and false explanation.

Q: Consider the following Digraph to answer the 1, 2 4 s W 3 1 S w 5 G 3 1. Find all possible paths…

A: We need to find all possible paths from the node s to T. Draw the adjacency matrix of the graph.

Q: Let G be a simple, undirected unweighted connected graph with n vertices and m edges, where m=…

A: Answer: (A) ------------ You can use Floyd - Warshall algorithm here. The Floyd - Warshall algorithm…

Q: 4.76. Suppose T is a minimal spanning tree found by Prim's algorithm in a connected graph G. (i)…

A: Let the graph G be connected, i.e. the answer exists. We denote by T the resulting graph found by…

Q: Let A, B, C, D be the vertices of a square with side length 100. If we want to create a…

Q: Suppose that G is an unconnected graph that consists of 4 connected components. The first component…

A: Euler Graph: A linked graph created by Euler. If there is a closed trail that contains every edge of…

Q: An undirected weighted graph G is given below: 12 2 6 Figure 16: An undirected weighted graph has 6…

A: The Answer is

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: Let DIST (u, v) denote the distance between vertex u and v. It is well known that distances in…

A: Given that, DIST(u, v) is the distance between the vertex u and v. If we consider any three vertices…

Q: ighted graph G with AT MOST 5 vertices which has at leas ees; wo different minimum spanning trees of…

A: Explained

Q: Using C++ programming language solve the following problem: You are given NN points in…

A: please see the next step for solution

Q: Let A, B, C, D be the vertices of a square with side length 100. If we want to create a…

A: The Answer is

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

Q: I claim that T1 and T2 must be identical spanning trees - i.e., the exact same set of edges must…

Q: Answer True or False to the following claims: a. If G is graph on at most 5 vertices and every…

A: Trees A tree is an undirected, linked, and acyclic graph in graph theory. It is a linked graph…

Q: a) Draw the connected subgraph of the given graph above which contains only four nodes ACGB and is…

A: In questions with many questions we must do the first one.

Q: Question 5 : Let there is an undirected graph with 10 nodes with the following edges (x-y means x…

A: Please check the step 2 for solution

Concept explainers

Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

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 |||
Problem 4: Consider the connected simple graph G given below. k Graph G 1. Use depth-first search to produce a spanning tree for the simple graph G. Choose vertex a as the root of this spanning tree. You must show how the spanning tree is constructed step by step as you add vertices and edges. Otherwise, your answer is wrong. Show your work step by step. 2. Use breadth-first search to produce a spanning tree for the simple graph G. Choose vertex a as the root of this spanning tree and assume that all vertices are ordered alphabetically. You must show how the spanning tree is constructed step by step as you add vertices and edges. Otherwise, your answer is wrong. Show your work step by step. 3. Is a spanning tree of a simple connected graph unique? Explain your answer clearly.
7. Consider the following graph: A 14 CO D 9 E C 12 10 17 b) What is the weight of the minimum spanning tree? B Apply Kruskal's algorithm to find the minimum spanning tree. Edges are sorted first by length, and in the event of a tie, by name, where the two letters are in alphabetical order. Use makeset (x), find (x), and union (x, y) to determine if there are cycles. a) Circle the edges that are part of the minimum spanning tree. AC, AD, AE, BC, BD, BE, DE c) Draw the tree that results from applying the union-find algorithm for cycle detection. When drawing the tree, put vertices with lower letters in the left subtrees so that all the vertices in a level are sorted alphabetically from left to right
b) Consider graph G=(V, E) with six nodes and eight edges. The edges have distinct integer weights. a 17 b 10 7 2 f 6 The minimum spanning tree of G is constructed by Kruskal's algorithm and is shown in tree MST below: a 17 101 10 7 C f d 6 The edge weights of only those edges that are in the MST are given in graph G. What is the minimum possible summation of edge weights for the edges (a, b), (e, d), (c, d)? (5 points) As you justify your answer for edge weights, please use graph G and apply Kruskal's algorithm to obtain the MST step by step (5 points). Show and explain all your work.
3. 4. Given a directed acyclic graph G = (V, E) and two vertices s, te V, design an efficient algorithm that computes the number of different directed paths from s to t. Define the incidence matrix B of a directed graph with no self-loop to be an nxm matrix with rows indexed by vertices, column indexed by edges such that Bij = -1 1 0 if edge j leaves vertex i, if edge jenters vertex i, otherwise. Let BT be the transpose of matrix B. Find out what the entries of the n x n matrix BBT stand for.
True or False (If your answer to the question is "False", explain why, and provide correction when possible). (a) Let h(n) be the heuristics for the node n, h(m) be the heuristics for the node m, d(m,n) be the actual minimal cost from node m to n in a graph. A* satisfies the monotone restriction iff d(m,n) <= |h(n)-h(m)|. (b) If an A* heuristics is admissible then it satisfies the monotone restriction. (c) Best-first search guarantees optimality in its returned solution. (d) Least-cost-first search guarantees optimality in its returned solution. (e) If all edges are with unit cost, then Breadth-first search guarantees optimality in its returned solution.
please answer both of the questions. 7. The Bellman-Ford algorithm for single-source shortest paths on a graph G(V,E) as discussed in class has a running time of O|V |3, where |V | is the number of vertices in the given graph. However, when the graph is sparse (i.e., |E| << |V |2), then this running time can be improved to O(|V ||E|). Describe how how this can be done.. 8. Let G(V,E) be an undirected graph such that each vertex has an even degree. Design an O(|V |+ |E|) time algorithm to direct the edges of G such that, for each vertex, the outdegree is equal to the indegree. Please give proper explanation and typed answer only.
Can you help me solve this exercise? Please note that the greedy approach described in the advice paragraph does not work.
Given N cities represented as vertices V₁, V2, un on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices vį and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). ... Assume that all edges have different values, and €₁,7 has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.
Given the following graph, A C 3 1 E 4 В F 7 D 5 What is the next edge and vertex(s) to be included in the solution if a. we are using Prim's algorithm to find a minimum spanning tree and we have started with vertex E? Edge: Vertex(s): What is the next edge and vertex(s) to be included in the solution if b. we are using Kruskal's algorithm to find a minimum spanning tree Edge: Vertex(s): What is the next edge and vertex(s) to be included in the solution if c. we are using Dijkstra's shortest path algorithm to find shortest paths and we have started with vertex E, with C and F already included in the shortest path tree? Edge: Vertex(s):
Let A, B, C, D be the vertices of a square with side length 100. If we want to create a minimum-weight spanning tree to connect these four vertices, clearly this spanning tree would have total weight 300 (e.g. we can connect AB, BC, and CD). But what if we are able to add extra vertices inside the square, and use these additional vertices in constructing our spanning tree? Would the minimum-weight spanning tree have total weight less than 300? And if so, where should these additional vertices be placed to minimize the total weight? Let G be a graph with the vertices A, B, C, D, and possibly one or more additional vertices that can be placed anywhere you want on the (two-dimensional) plane containing the four vertices of the square. Determine the smallest total weight for the minimum-weight spanning tree of G. Round your answer to the nearest integer. Attention: Please don't just copy these two following answers, which are not correct at all. Thank you.…
Given N cities represented as vertices V₁, V2,..., UN on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices v; and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). Assume that all edges have different values, and e₁, has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.