Given the following adjacency matrix representing a graphv1 v2 V3 V4 v5 v6v1 0 1 0 0 1 0v2 0 o 1 0 10v3 0 0 0 1 0 0v4 0 0 1 ov5 0 0 0V6 0 0 0 111The order of vising DFS starting from vertex V1 isа.None of themОБ. 1,2, 5, 4, 6, 3Ос. 1,2, 3,4, 5, 6d. 1, 5, 3, 4, 2, 61.

We have given an Adjacency matrix and we have to find the order of visiting DFS starting from the…

Answered: Given the following adjacency matrix…

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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Discrete mathematics. Let G = (V, E) be a simple graph4 with n = |V| vertices, and let A be its adjacency matrix of dimension n × n. We want to count the L-cycles : such a cycle, denoted by C = u0u1 · · · uL with uL = u0 contains L distinct vertices u0, . . . , uL-1 et L edges E(C) = {uiui+1 | 0 ≤ i ≤ L − 1} ⊆ E. Two cycles are distinct if the edge sets are different : C = C' if and only if E(C) = E(C'). We define the matrices D, T, Q, the powers of A by matrix multiplication : D = A · A = A2, T = A · D = A3, Q = A · T = A4. Consider the values on the diagonals. Prove that for any vertex u ∈ V with degree d(u), d(u) = Du,u.
Assume a graph G is simple (ie. no self loop or parallel edges) .Let v be any vertex in the graph. Let boolean[] marked be initalized to all false. Consider: boolean dfs(Graph G, int v) { marked[v] = true; for (int w : G.adj(v)) { if (w == u) continue; if (marked[w]) return true; if (dfs (G, v, w)) return true; } return false; } If the call dfs(v) returns true, then: a. The graph has cyclesb. The graph is bipartitec. The graph is connected
P R O B L E M D E S C R I P T I O N :1. As described in the reading and lecture, an adjacency matrix for a graph with n verticesnumber 0, 1, …, n – 1 is an n by n array matrix such that matrix[i][j] is 1 (or true) ifthere is an edge from vertex i to vertex j, and 0 (or false) otherwise.2. In this assignment, you will implement the methods identified in the stub code below insupport of the Graph ADT that uses an adjacency matrix to represent an undirected,unweighted graph with no self-loops.import java.util.*; // for all needed JCF classespublic class Graph { private int[][] matrix;// the adjacency matrix of the graph. // Creates an n x n array with all values initialized to 0. public Graph(int n) {// your code here } // end constructor // This method returns the number of nodes in the graph. public int getNumVertices() {// your code here } // end getNumVertices // This method returns the number of edges in the graph. public int getNumEdges() {// your code here } // end getNumEdges //…
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…
let g be the following dierected graph
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)}
Trace through of Dijkstra's Algorithm, using vertex v5 as the source vertex. Here is adjacency matrix representing the graph with n = 6 vertices: 1 2 3 4 5 6 1 0 999 5 8 999 4 2 9 0 999 999 12 3 3 999 10 0 2 9 999 4 999 999 999 0 999 999 999 7 17 999 0 11 6 5 999 11 16 2 0 Initially we have: vnear= 5. Fill array performing initiation. touch length 1 2 3 4 5 6 Repeat the main loop 5 times: Hint: copy and paste following table five times, then fill all values for arrays. Vnear = 1 2 3 4 5 6 touch length
Consider the following edge-weighted graph G with 9 vertices and 16 edges: 90 Q6.1 Kruskal 40 50 80 130 110 70 S 150 60 30 10 120 140 20 100 List the weights of the MST edges in the order that Kruskal's algorithm adds them the MST. Your answer should be a sequence of 8 integers, with one space between each integer, 14
Pick the correct statements for the attached directed graph for a toy world wide web. 1. There are exactly six columns having a 1 as an entry. 2. If a new edge from node I to F is added, the resulting graph is strongly connected. 3. The smallest non-zero element in the link matrix is 1/4. 4. The link matrix Q has a column of all zeros. 5. The link matrix is a reducible matrix.
Consider the following weighted undirected graph. 9 A В 8. 10 11 14 F 5 16 15 G H 12 13 We would like to run the Prim's algorithm on this graph using A as initial vertex. List the edges appearing in the Minimum Spanning Tree (MST) in the order they are added to the MST.
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…
Given the graph below, list the vertex visitation order of a depth-first search (DFS) beginning at vertex A. [follow alphabetical order] * B D E F H. O A>B>C>E>D>F>H>l>G O A>B>C>F>D>E>H>G>l O A>B>C>F>D>E>l>H>G A>B>C>E>F>G>H>l>D Other:

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Given the following adjacency matrix representing a graph v1 v2 v3 V4 v5 v6 v1 0 1 0 0 10 v2 0 0 1 0 1 0 v3 0 0 0 1 0 0 V4 0 0 1 0 V5 0 0 V6 0 0 0 100 The order of vising DFS starting from vertex V1 is O a. None of them O b. 1, 2, 5, 4, 6, 3 O . 1, 2, 3, 4, 5, 6 d. 1, 5, 3, 4, 2, 6 1.