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

See similar textbooks

Similar questions

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.
During the execution of DFS, give the conditions under which there is an edge from a vertex u with color c1 has an edge to a vertex v with color c2. Consider the following color combinations, (c1, c2)= (w,w), (w,g), (g, b) and (b,g).
Given a vertex set W = {1, 2, 3, 4}, solve for the following questions: (i) Knowing that edges are the same if and only if they have the same endpoint, how many different edges are possible? (ii) Suppose for this question that graphs are different if they have different sets of edges (they do not depend on if the graphs are isomorphic or not). How many simple graphs are there with the vertex set W? (iii) Draw the eleven nonisomorphic simple graphs that have four vertices.
Let G be a connected graph with n vertices and m edges.Which of the following statements are true?(i) G is a tree if and only if n = m+1.(ii) G is a tree if and only if m = n+1.(iii) G is a tree if and only if the addition of any edgeto G will produce a unique cycle.(iv) G is a tree if and only if G contains at least onepath b etween any two vertices.(v) If G is connected, then G is a tree if and only if Gcontains at most one path between any two vertices.(vi) A connected subgraph of a tree is always a tree.
Let G be a graph with 7 vertices, where eachvertex is labelled by a number from 1 to 7. Twovertices are selected at random. Let us call themu and v. Now, directed edges are drawn from u toall other vertices except v and directed edges aredrawn from all vertices to v except from u. Let xbe the total possible topological sortings of G.hint: You may remember the terms factorials orfibonacci?Write down the value of x:
How many undirected graphs (not necessarily connected) can be constructed out of a given set V= {V 1, V 2,…V n} of n vertices ? Group of answer choices 2^(n(n-1)/2) 2^n n(n-l)/2 n! Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? Adding a vertex in adjacency list representation is easier than adjacency matrix representation. In adjacency list representation, space is saved for sparse graphs. DFS and BSF can be done in O(V + E) time for adjacency list representation. These operations take O(V^2) time in adjacency matrix representation. Here is V and E are number of vertices and edges respectively. All of the above Given the starting vertex A, what is the visit order of the graph shown in Fig. 1 under the DFS traversal algorithm. ABDCFE ACBDFE ABCDFE ADBCEF Assume you have the adjacency matrix representing a graph. 1 represents a connection while -1 represents a lack of one:[-1, 1, - 1][-1, -1, 1][1, -1,…
If removing any 3 vertices from a connected graph G keeps it connected then: A- G must be 4-vertex connected B-G must be 3-vertex connected C-The edge connectivity of G must be at least 4 D-The vertex connectivity of G must be at least 4
For each graph representation, select the appropriate worst-case time complexity for printing the vertex label of all the neighbors of a given vertex. Assume that vertex label retrieval from a typical integer vertex representation is O(1). Adjacency Matrix: ________ Edge List: ________ Adjacency List: _________ Choices: O(V+E), O(E^2), O(V^2), O(E)
The Algorithm of AlgebraThe adjacency matrix A of a graph G = is used by the algebraic BFS algorithm (V, E).First, we create a vector x with all zeros except for the index of the source vertex s that we wish to use as the starting point for the algorithm; next, we create the matrix A = A+ I; last, AT x chooses all nodes that are at a distance of 1 (level 1) from the source vertex. The vertices with the fewest number of hops are obtained by multiplying the vector x by the matrix A2. As a rule, the product Ak x will produce neighbours that are at most k hops distant, and the multiplication should be done in a boolean manner as in the algorithm shown below. Algorithm for Algebraic BFS1: Input : Adjacency matrix An,n of a graph G = (V, E) connected, unweighted graph G and asource vertex s2: Output : N, visited, levels a matrix that shows level i vertices at its column i, the visitedvertices in sequence and their levels3: x[n] ← 04: x[s] ← 15: A ← A + I6: for i = 1 to n do7: N ← AT · x8:…
Let G be an undirected graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex be given by the table below: look at the picture sent 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 above. Which statement of the following is correct? group of answer choices a) The sequence of vertices visited using a DFS traversal starting at vertex 1: 1, 2, 3, 4, 6, 5, 7, 8. b) The sequence of vertices visited using a BFS traversal starting at vertex 1: 1, 2, 3, 4, 6, 5, 7, 8. c) Both sequences are wrong. d) Both sequences are correct.
I need help in this question of Graph based on the Screenshot attached URGENT ASAP! True or False a)After executing BFS( G2, A ), the parent of vertex C is vertex A. b)After executing DFS( G2, G ), the parent of vertex D is vertex B. c)After executing DFS( G2, G ), vertex F is a leaf in the DFS-tree. d)After executing DFS( G2, A ), the parent of vertex D is vertex C.
Throughout, a graph is given as input as an adjacency list. That is, G is a dictionary where the keysare vertices, and for a vertex v,G[v] = [u such that there is an edge going from v to u].In the case that G is undirected, for every edge u − v, v is in G[u] and u is in G[v]. 3. Write the full pseudocode for the following problem.Input: A directed graph G, and an ordering on the vertices given in a list A.Output: Is A a topological order? In other words, is there an i, j such that i < j and there is an edge fromA[j] to A[i]?

SEE MORE QUESTIONS

Recommended textbooks for you

Database System Concepts

Computer Science

ISBN:

9780078022159

Author:

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

Publisher:

McGraw-Hill Education

Starting Out with Python (4th Edition)

Computer Science

ISBN:

9780134444321

Author:

Tony Gaddis

Publisher:

PEARSON

Digital Fundamentals (11th Edition)

Computer Science

ISBN:

9780132737968

Author:

Thomas L. Floyd

Publisher:

PEARSON

Database System Concepts

Computer Science

ISBN:

9780078022159

Author:

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

Publisher:

McGraw-Hill Education

Starting Out with Python (4th Edition)

Computer Science

ISBN:

9780134444321

Author:

Tony Gaddis

Publisher:

PEARSON

Digital Fundamentals (11th Edition)

Computer Science

ISBN:

9780132737968

Author:

Thomas L. Floyd

Publisher:

PEARSON

C How to Program (8th Edition)

Computer Science

ISBN:

9780133976892

Author:

Paul J. Deitel, Harvey Deitel

Publisher:

PEARSON

Database Systems: Design, Implementation, & Manag…

Computer Science

ISBN:

9781337627900

Author:

Carlos Coronel, Steven Morris

Publisher:

Cengage Learning

Programmable Logic Controllers

Computer Science

ISBN:

9780073373843

Author:

Frank D. Petruzella

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS

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.