C.The base function f(x) is reflected in the x-axis, stretched elly by aand translated 3 units to the left and 1 unit down Witte the equation of thefunction g(x) (4 marks).Given the graph of f(x), graph each of the following clearly labeling each graph:(2 marks each)a.f(-x)f-¹(x)ter of 2.foredb.

Answered: Image /qna-images/answer/deb060b5-5612-46ab-9198-da7df7cb6b7a.jpg

7. 6. The base function f(x) is reflected in the and translated 3 units to the left and 1 unit down Witte the equation of the inst function g(x) (4 marks). Given the graph of f(x), graph each of the following clearly labeling each graph: (2 marks each) f(-x) a. f-1(x) b.

7. 6. The base function f(x) is reflected in the and translated 3 units to the left and 1 unit down Witte the equation of the inst function g(x) (4 marks). Given the graph of f(x), graph each of the following clearly labeling each graph: (2 marks each) f(-x) a. f-1(x) b.

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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c) Find a Hamiltonian Cycle starting at vertex A. Draw the Hamiltonian Cycle on the graph and list the vertices of the cycle. K L M A B E F G H J Note: A Hamiltonian Cycle is a simple cycle that traverses all vertices. A simple cycle starts at a vertex, visits other vertices once then returns to the starting vertex. For instance, if the vertices of Ks were labeled A, B, C, D, E, one Hamiltonian Cycle would be ABCDEA.
a) Illustrate the sequence of vertices of this graph visited using depth-first search traversal starting at vertex g. b) Illustrate adjacency list representation and adjacency matrix representation, respectively, for this graph. What are the advantages and disadvantages of those two representations? c) Describe an algorithm to find in the graph a path illustrated below that goes through every edge exactly once in each direction.
2. (15 pts.) the adjacency matrix of G. Let n be the number of vertices so that the matrix M is n x n matrix. For any matrix A, let us denote the element of i-th row and j-th column of the matrix A by A[i, j]. We are given a graph G = (V, E); G could be a directed graph or undirected graph. Let M be 1. Consider the square of the adjacency matrix M. For all i and j, show that M²[i, j] is the number of different paths of length 2 from the i-th vertex to the j-th vertex. It should be explained or proved as clearly as possible. 2. For any positive integer k, show that Mk[i, j] is the number of different paths vertex to the j-th vertex. You may use induction on k to prove it. length k from the i-th 3. Assume that we are given a positive integer k. Design an algorithm to find the number of different paths of length k from the i-th vertex to j-th vertex for all pairs of (i, j). The time complexity of your algorithm should be O(n³ log k). You can get partial credits if you design an algorithm…
Artificial Inteligence
(a) Let G be a simple undirected graph with 18 vertices and 53 edges such that the degreesof G are only 3 and 7. Suppose there are a vertices of degree 7 and b vertices ofdegree 3. Find a and b. To receive any credit for this problem you must write completesentences, explain all of your work, and not leave out any details. problem 1, continued(b) Recall that a graph G is said to be k-regular if and only if every vertex in G has degreek. Draw all 3-regular simple graphs with 12 edges (mutually non-isomorphic). Hint:there are six of them. To receive credit for this problem, you should explain, as well aspossible, why all of your graphs are mutually non-isomorphic.
w describe the Python code for the 2-approximation algorithm. The main part of the code deals with deleting the randomly selected edge from the graph along with its neighboring edges. Input to the procedure VC_Approx is the incidence matrix B(G) of the graph G. The unmarked edges are held in the list edges and the endpoints of a selected edge are included in the list V C at each iteration. The incidence matrix B of the graph is input and we find adjacent edges to the matched edge by iterating through rows of B. Each found edge is deleted from the list edges and main while loop iterates until this list becomes empty. We check adjacent edges to the matched edge from this matrix by deleting adjacent edges at each endpoint.
10. Consider the statement “Every connected graph has one or more vertices of degree 2." Each of the five graphs below has one or more connected components. Which of the five graphs is a counterexample to the statement? (A) (B) (C) (D) AA "I 1 (E)
Source:https://www.mog.dog/files/SP2019/Sipser_Introduction.to.the.Theory.of.Computation.3E.pdf
Please solve with the computer Question 2: Draw a simple undirected graph G that has 11 vertices, 7 edges.
Problem 3 1) Consider that you have a graph with 8 vertices numbered A to H, and the following edges: (A, B), (A, C), (B, C), (B, D), (C, D), (C, E), (D, E), (D, F), (E, G), (F, G), (F, H), (G, H) a) Using depth-first search algorithm, what would be the sequence of visited nodes starting at A (show the content of the stack at some steps). b) Same question if the algorithm used in breadth first search. c) What would be the minimum spanning tree rooted at A if a Depth First Search algorithm is used (refer to question a), show few steps in running the algorithm. d) What would be the minimum spanning tree if a Breadth First Search algorithm is used (refer to question b), show few steps of the algorithm.
(i) Write a C program to implement an algorithm based on Depth-First Search to test the connectivity of a given network. Input: Adjacency matrix (refer to sample program on page 6 for reading in an adjacency matrix) Output: The sequence that vertices are being visited The vertices of each connected component of a given graph The parent of each vertex (a vertex p is the parent of vertex c if c is visited from p) Note: To mark a vertex to indicate if has been visited or not, a one-dimensional integer array, say visit[maxV], where maxV is the size of the array, could be used. visit[i] is set to 0 initially for all i (unvisited), and is set to 1 if visited.
Q.3 (a) Find the degree sequence of the graphs: K6,5, W, (b) Find All values of n such that the graphs: (i) K. (i) C are bipartite (c) Draw the graph with the given incidence matrix 1 100 1011 1 1 100 00 0 01 1001 0 0011 10 0 00 00 0ol Thope the solution is clear and the line is understandable