Suppose F, G and H are simple graphs.
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Suppose F, G and H are simple graphs. Suppose f is an isomorphism from F to G and g is an isomorphism from G to H. Which of the following functions h is an isomorphism from F to H?
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- 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.(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?The homomorphism h is defined by h(a) = 01 and h(b) = 10. What is h(%%1%%2%%3%%4)?
- (V, E) be a connected, undirected graph. Let A = V, B = V, and f(u) = neighbours of u. Select all that are true. Let G = a) f: AB is not a function Ob) f: A B is a function but we cannot always apply the Pigeonhole Principle with this A, B Odf: A B is a function but we cannot always apply the extended Pigeonhole Principle with this A, B d) none of the above5. (This question goes slightly beyond what was covered in the lectures, but you can solve it by combining algorithms that we have described.) A directed graph is said to be strongly connected if every vertex is reachable from every other vertex; i.e., for every pair of vertices u, v, there is a directed path from u to v and a directed path from v to u. A strong component of a graph is then a maximal subgraph that is strongly connected. That is all vertices in a strong component can reach each other, and any other vertex in the directed graph either cannot reach the strong component or cannot be reached from the component. (Note that we are considering directed graphs, so for a pair of vertices u and v there could be a path from u to v, but no path path from v back to u; in that case, u and v are not in the same strong component, even though they are connected by a path in one direction.) Given a vertex v in a directed graph D, design an algorithm for com- puting the strong connected…Computer Science In function f(x) ->y the domain of x is continuous in the range 1-10how many equivalence classes are there in this case?
- 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 approachWrite a C program to Find disjoint sets in a graph using disjoint set ADT operations FIND, UNIONLet us first discuss what disjoint sets in a graph is? Disjoint sets in a graph mean components of a graph. Each connected component is treated as a disjoint set since it has no relation with the other components. Each connection (edge) is said to be the relation between two nodes. Two nodes having a relation falls in the same set. The algorithm is:For each edge in the edge list:If the nodes on the edge are in same set, do nothing, otherwise, we will UNION them as they have relations between them and should come under same set.To check whether the two nodes are in same set we use FIND NOTE: IN C PROGRAM ONLY PLEASE Output: (attached picture)The Graph Data Structure is made up of nodes and edges. (A Tree Data Structure is a special kind of a Graph Data Structure). A Graph may be represented by an Adjacency Matrix or an Adjacency List. Through this exercise, you should be able to have a better grasp the Adjacency Matrix concept. You are expected to read about the Adjacency Matrix concept as well as the Adjacency List concept. Suppose the vertices A, B, C, D, E, F, G and H of a Graph are mapped to row and column indices(0,1,2,3,4,5,6,and 7) of a matrix (i.e. 2-dimensional array) as shown in the following table. Vertex of Graph Index in the 2-D Array Adjacency Matrix Representation of Graph A B 2 F 6. H 7 Suppose further, that the following is an Adjacency Matrix representing the Graph. 3 4 5. 6. 7 0. 1 1 1 1 01 1 01 1. 3 14 1 1 1 6. 1 Exercise: Show/Draw the Graph that is represented by the above Adjacency matrix. Upload the document that contains your result. (Filename: AdjacencyMatrixExercise.pdf) Notes: -The nodes of the…
- Write a program (WAP) in c to create an undirected graph using adjacency matrix representation.Number of nodes and edges should be taken from the user. After creating the graph, performfollowing operations: (i) Search a node. Take the node number from the user. If the node is found then print its associatededges.(ii) Insert a node in the graph.(iii) Insert an edge in the graph. Take the node numbers from the user between which the edge is tobe inserted.(iv) Delete a node from the graph. Take the node number to be deleted from the user.(v) Apply DFS on the graph and print the graph traversal.(vi) Apply BFS on the graph and print the graph traversal.2. Solve the above problem using adjacency list representation.3) The graph k-coloring problem is stated as follows: Given an undirected graph G= (V,E) with N vertices and M edges and an integer k. Assign to each vertex v in V a color c(v) such that 1Problem 1. For each of the following graphs G = (V, E), a. V = {a, b, c, d, e}, E = {[a, b], [a, c], [a, d], [a, e]}. b. V = {a, b, c, d, e), E = {[a, b], [b, c], [c, d], [d, a]}, c. V = {a, b, c, d, e, f}, E = {[a, b], [(b, c], [c, a], [d, e], [e, fl}, d. V = (a, b, c, d, e, f), E = {[a, b], [b, c], [c, a], [d, e], [e, f], [f, a]}, e. V = {a,b,c}, E = {}. (i) sketch the graph, (ii) give an explicit expression for each connected component, and (iii) say whether the graph is a tree or a forest. metric spaces (X, d),SEE MORE QUESTIONS