4. Graphs represented in Adjacency Matrices 5. True or False: If G is a complete graph (i.e. each pair of vertices is connected byan edge) containing 5 vertices, then B(G) has more elements than an adjacencymatrix representation of G .6. True or False: If G is a tree containing 5 vertices, then B(G) has more elementsthan an adjacency matrix representation of G . Let G be an undirected, connected graph with vertex set V(G) = {V₁, V2, ..., Vn}and edge set E(G) = {e₁,e2, ..., em}.Let B(G) = [bj] be an n x m matrix in which the (i, j)-th element b;; = 1 if v; isone of the end vertices of e; and 0 otherwise.Fill in the blanks below. If it is a True-or-False type question, place a T or F,respectively.4. For an undirected, connected graph G with n vertices and m edges, the size ofB(G) is ().

4. Size of B(G) is θ(n*m) This is because the matrix has n rows and m .columns

5. True or False: If G is a complete graph (i.e. each pair of vertices is connected by an edge) containing 5 vertices, then B(G) has more elements than an adjacency matrix representation of G. 6. True or False: If G is a tree containing 5 vertices, then B(G) has more elements than an adjacency matrix representation of G .

5. True or False: If G is a complete graph (i.e. each pair of vertices is connected by an edge) containing 5 vertices, then B(G) has more elements than an adjacency matrix representation of G. 6. True or False: If G is a tree containing 5 vertices, then B(G) has more elements than an adjacency matrix representation of G .

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

Similar questions

Let V= {cities of Metro Manila} and E = {(x; y) | x and y are adjacent cities in Metro Manila.} (a) Draw the graph G defined by G = (V; E). You may use initials to name a vertex representing a city. (b) Apply the Four-Color Theorem to determine the chromatic number of the vertex coloring for G.
Create a graph containing the following edges and display the nodes of a graph in depth first traversal and breadth first traversal. V(G) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} E(G) = {(0, 1), (0, 5), (1, 2), (1, 3), (1, 5), (2, 4), (4, 3), (5, 6), (6, 8), (7, 3), (7, 8), (8, 10), (9, 4), (9, 7), (9, 10)} The input file should consist of the number of vertices in the graph in the first line and the vertices that are adjacent to the vertex in the following lines. Header File #ifndef H_graph #define H_graph #include <iostream> #include <fstream> #include <iomanip> #include "linkedList.h" #include "unorderedLinkedList.h" #include "linkedQueue.h" using namespace std; class graphType { public: bool isEmpty() const; void createGraph(); void clearGraph(); void printGraph() const; void depthFirstTraversal(); void dftAtVertex(int vertex); void breadthFirstTraversal(); graphType(int size = 0); ~graphType(); protected: int maxSize; //maximum number of…
4. Let G=(V, E) be the following undirected graph: V = {1, 2, 3, 4, 5, 6, 7, 8} E = {(1, 7) (1, 4), (1, 6), (6, 4), (7, 5), (2, 5), (2, 4), (4, 3), (4, 8), (8, 3), (3, 5)}. a. Draw G. b. Is G connected? c. Give the adjacency matrix for the graph G given above. d. Determine whether the graph has a Hamiltonian cycle. If the graph does have a Hamiltonian cycle, specify the nodes of one. If it does not, prove that it does not have one. e. Determine whether the graph has a Euler cycle. If the graph does have a Euler cycle, specify the nodes of one. If it does not, prove that it does not have one.
Be G=(V, E)a connected graph and u, vEV. The distance Come in u and v, denoted by d(u, v), is the length of the shortest path between u'and v, Meanwhile he width from G, denoted as A(G), is the greatest distance between two of its vertices. a) Show that if A(G) 24 then A(G) <2. b) Show that if G has a cut vertex and A(G) = 2, then Ġhas a vertex with no neighbors.
Write a Java program to find the Adjacency Matrix Representation using Directed Graph. а. Insert new nodes and directed edge between two nodes b. Display the representation
Represent the following graph using an edge array, a list of edge objects, an adjacency matrix, an adjacency vertex list, and an adjacency edge list, respectively. 1 3 2
draw the graph that represents said matrix and find out, using Python, the number of 3-paths that connect the vertices v1 and v3 of the same.
Let G be a graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex be given by the table. Assume that, in a traversal of G, the adjacent vertices of a given vertex are returned in the same order as they are listed in the table below. Vertex Adjacent vertices 1 2 3 4 5 6 7 8 (2,3,4) (1,3,4) (1,2,4) (1,2,3,6) (6,7,8) (4,5,7) (5,6,8) (5,7) a) Draw Gb) Order the vertices as they are visited in a DFS traversal starting at vertex 1. c) Order the vertices as they are visited in a BFS traversal starting at vertex 1.
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
Draw a graph G containing the following vertices and edges. V(G) = {0, 1, 2, 3, 4, 5, 6} E(G) = { (0, 1), (0, 2), (0, 3), (2, 1), (2, 4), (5, 1), (5, 3)}
A directed graph G is defined using the following sets of vertices and edges. {n1, n2, n3, n4, N5, n6, n7, ng } E = {, , , , , , , , , } Q4) V = a) What is the adjacency matrix of G? b) List all semipaths of length 2 and 3. c) Give the condensation graph of G.
5. Vertices: (a, b, c, d, e, f, g) Edges: {(a, b), (a, f), (b, e), (b, g). (c. f). (c. g). (c. d), (d. e), (d. g} } Draw a Graph for the given vertices and edges. Find the adjacent vertices of a vertex c. Find the shortest path between source vertex f and destination vertex e.