Given this directed graph, which of the following statements is false?12345678There is a circuit of length 5 starting at vertex 2.There is a path of length 4 from vertex 5 to vertex 3.There is a walk of length 5 from vertex 5 to vertex 7.There is a cycle of length 3 starting at vertex 5.

Important Notes to Remember in this problem:Walk: A sequence of edges, where the start and end…

Answered: Given this directed graph, which of the…

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

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Suppose you have a graph G with 6 vertices and 7 edges, and you are given the following information: The degree of vertex 1 is 3. The degree of vertex 2 is 4. The degree of vertex 3 is 2. The degree of vertex 4 is 3. The degree of vertex 5 is 2. The degree of vertex 6 is 2. What is the minimum possible number of cycles in the graph G?
Consider the graph depicted above. Decide whether the following statements are true (T) or false (F): The sequence <a, b, f, d> is a circuit There is a path of length 7 in the graph above In the graph above there is a walk of length 10 that involves only the nodes a and b The sequence <a, b, c, f, h> is a walk The longest path in the graph is of length 9
Here are two new definitions about graphs. The distance between two vertices in a graph is the number of edges in a shortest path connecting them. The diameter of a graph is the greatest distance between any pair of vertices in the graph. 1. What is the diameter of the cycle C13? What is the diameter of the cycle C₁4? 2. What is the diameter of the path Pg? 3. What is the diameter of the compelte graph K4? 4. What is the diameter of the complete bipartite graph K3,4? GI → J-> J
Consider the following graph G. Which vertices of G have degree equal to 2. 0 0 A A B C D E F G t u B V с W D E X TI F y N G
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One can manually count path lengths in a graph using adjacency matrices. Using the simple example below, produces the following adjacency matrix: A B A 1 1 B 1 0 This matrix means that given two vertices A and B in the graph above, there is a connection from A back to itself, and a two-way connection from A to B. To count the number of paths of length one, or direct connections in the graph, all one must do is count the number of 1s in the graph, three in this case, represented in letter notation as AA, AB, and BA. AA means that the connection starts and ends at A, AB means it starts at A and ends at B, and so on. However, counting the number of two-hop paths is a little more involved. The possibilities are AAA, ABA, and BAB, AAB, and BAA, making a total of five 2-hop paths. The 3-hop paths starting from A would be AAAA, AAAB, AABA, ABAA, and ABAB. Starting from B, the 3-hop paths are BAAA, BAAB, and BABA. Altogether, that would be eight 3-hop paths within this graph. Write a program…
Given a cycle graph Cn and a complete graph Kn on n vertices (n>3), select all the correct statements. The degree of each vertice in Cn is 2 The total number of edges in Kn is C(n, 2). The degree of each vertice in Kn is (n-1). The total number of edges in Cn is n.
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2. Use the following description of an undirected graph and draw the graph: v(Graph1) = { A, B, C, D} E(Graph1) = { (A,B), (A,D), (B,C), (B,D) }
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Select the graph that is not regular. в D B D D C A B

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