For the following directed graph, let E = {I,J,K,L,M} and let V = {a,b, c, d}. %3D a d M b K For each definition of f below, determine if f is a function. If it is a function, state its domain and codomain in the form “f:X → Y" and give a table of values that lists eac element x of the domain along with the corresponding element f(x) of the codomai If the given f is not a function, explain why not.

For the following directed graph, let E = {I,J,K,L,M} and let V = {a,b, c, d}. %3D a d M b K For each definition of f below, determine if f is a function. If it is a function, state its domain and codomain in the form “f:X → Y" and give a table of values that lists eac element x of the domain along with the corresponding element f(x) of the codomai If the given f is not a function, explain why not.

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

PLEASE ANSWER ALL PARTS OF THIS QUESTION. For the following directed graph, let ? = {?,?,?, ?, ?} and let ? = {?, ?, ?, ?}. For the definition of ? below, determine if ? is a function. If it is a function, state its domain and codomain in the form “?:? → ?” and give a table of values that lists each element ? of the domain along with the corresponding element ��(?) of the codomain. If the given ? is not a function, explain why not. If ? is a vertex, then ?(?) is the indegree of ?.
Question 1: In graph theory, a graph X is a "complement" of a graph F if which of the following is true? Select one: a. If X is isomorph to F, then X is a complement of F. b. If X has half of the vertices of F (or if F has half of the vertices of X) then X is a complement of F. c. If X has the same vertex set as F, and as its edges ONLY all possible edges NOT contained in F, then X is a complement of F. d. If X is NOT isomorph to F, then X is a complement of F. Question 2: Which statement is NOT true about Merge Sort Algorithm: Select one: a. Merge Sort time complexity for worst case scenarios is: O(n log n) b. Merge Sort is a quadratic sorting algorithm c. Merge Sort key disadvantage is space overhead as compared to Bubble Sort, Selection Sort and Insertion Sort. d. Merge Sort adopts recursive approach
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]?
2. Let G = (V, E) be a directed weighted graph with the vertices V = {A, B, C, D, E, F) and the edges E= {(A, B, 12), (A, D, 17), (B, C, 8), (B, D, 13), (B, E, 15), (B, F, 13), (C, E, 12), (C, F, 25)}, where the third components is the cost. (a) Write down the adjacency list representation the graph G = (V, E).
A network is considered to be biconnected if every pair of its vertices is linked by two distinct paths. A vertex that, if it and its surrounding edges were removed, would result in the graph becoming unconnected is known as an articulation point in a linked network. show any graph without articulation points that it is biconnected. Use the fact that none of the vertices on the path is an articulation point to construct two disjoint paths connecting s and t given a set of vertices s and t and a path connecting them.
Every pair of vertices in a graph that is linked by two different paths is said to be biconnected. An articulation point in a connected graph is a vertex that, if it and its surrounding edges were eliminated, would cause the graph to become disconnected. demonstrate the biconnection of any graph lacking articulation points. Tip: To create two disjoint paths connecting s and t given a set of vertices s and t and a path connecting them, take advantage of the fact that none of the vertices on the path are articulation points.
For each pair of graphs G1 = <V1, E1> and G2 = <V2, E2> a) determine if they are isomorphic or not. b) Determine a function that can be isomorphic between them if they are isomorphic. Otherwise you should justify why they are not isomorphic. c) is there an Euler road or an Euler bike in anyone graph? Is Hamilton available? You should draw if the answer is yes and reason if your answer is no.
For the following simple graphs G=(V,E) (described by their vertex and edge sets) decide whether they are bipartite or not. If G is bipartite, then give its bipartition, and if it is not explain why. 1) V={a,b,c,d,e,f,g}, E={ag,af,ae,bf,be,bc,dc,dg,df,de} 2) V={a,b,c,d,e,f,g,h}, E={ac,ad,ah,bc,bh,bd,ec,ef,eg,hf,hg}
The boolean formula is given as follows. F = (a v b) ^ (a' v b') ^ (c V b') ^ (a' v b) a. Turn the formula into a directed graph and determine if it is satisfiable or unsatisfiable using a strongly connected component (SCC) search! (If there is a variable and complement for example: a and a', in one SCC then it can be concluded that the formula is unsatisfiable)
Write a boolean function, called universalSink, to determine weather a directed graph has a universal sink. A universal sink is a vertex which has no outgoing edges, and all other vertices have an incoming edge to the sink vertex. Hint: it has to be a C++ function
(a) Give the definition of an isomorphism from a graph G to a graph H. (b) Consider the graphs G and H below. Are G and H isomorphic?• If yes, give an isomorphism from G to H. You don’t need to prove that it isan isomorphism.• If no, explain why. If you claim that a graph does not have a certain feature,you must demonstrate that concretely. (c) Consider the degree sequence (1, 2, 4, 4, 5). For each of the following, ifthe answer is yes, draw an example. If the answer is no, explain why. (i) Does there exist a graph with this degree sequence?(ii) Does there exist a simple graph with this degree sequence?
please answer both of the questions. 7. The Bellman-Ford algorithm for single-source shortest paths on a graph G(V,E) as discussed in class has a running time of O|V |3, where |V | is the number of vertices in the given graph. However, when the graph is sparse (i.e., |E| << |V |2), then this running time can be improved to O(|V ||E|). Describe how how this can be done.. 8. Let G(V,E) be an undirected graph such that each vertex has an even degree. Design an O(|V |+ |E|) time algorithm to direct the edges of G such that, for each vertex, the outdegree is equal to the indegree. Please give proper explanation and typed answer only.