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.
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- Given the following adjacency matrix representing a graph V1 V2 V3 V4 V5 V6 V1 0 0 1 0 0 0 V2 0 0 1 0 1 0 V3 0 0 0 1 0 0 V4 0 1 0 0 0 1 V5 0 0 0 1 0 0 V6 1 0 0 0 0 0 The order of vising DFS starting from vertex V1 is O a. 1, 3, 4, 2, 5, 6 O b. 1, 2, 5, 4, 3, 6 O c. 1, 5, 3, 4, 6 O d. None of themConstruct all regular graphs that exist for the vertex set V = {1, 2, 3, 4}. For example, G = (V,E0) where E0 = {} is one possible graphTo help jog your memory, here are some definitions: Vertex Cover: given an undirected unweighted graph G = (V, E), a vertex cover Cy of G is a subset of vertices such that for every edge e = (u, v) = E, at least one of u or v must be in the vertex cover Cy. Set Cover: given a universe of elements U and a collection of sets S = {S₁, ..., Sm}, a set cover is any (sub)collection C's whose union equals U. In the minimum vertex cover problem, we are given an undirected unweighted graph G = (V, E), and are asked to find the smallest vertex cover. For example, in the following graph, {A, E, C, D} is a vertex cover, but not a minimum vertex cover. The minimum vertex covers are {B, E, C} and {A, E, C}. A B E с F D Then, recall in the minimum set cover problem, we are given a set U and a collection S = {S₁, ..., Sm} of subsets of U, and are asked to find the smallest set cover. For example, given U := {a, b, c, d}, S₁ := {a, b,c}, S₂ = = {b,c}, and S3 := {c, d), a solution to the problem is C's…
- 3. From the graph above determine the vertex sequence of the shortest path connecting the following pairs of vertex and give each length: a. V & W b. U & Y c. U & X d. S & V e. S & Z 4. For each pair of vertex in no. 3 give the vertex sequence of the longest path connecting them that repeat no edges. Is there a longest path connecting them?An undirected weighted graph G is given below Figure 16: An undirected weighted graph has 6 vertices, a through f, and 9 edges. Vertex d is on the left. Vertex f is above and to the right of vertex d. Vertex e is below and to the right of vertex f, but above vertex d. Vertex c is below and to the right of vertex e. Vertex a is above vertex e and to the right of vertex c. Vertex b is below and to the right of vertex a, but above vertex c. The edges between the vertices and their weight are as follows: d and f, 1; d and e, 4; f and e, 2; e and a, 2; f and a, 3; e and c, 5; c and a, 7; c and b, 5; and a and b, 6. (a) What is the minimum weight spanning tree for the weighted graph subject to the condition that edge {d, e} is in the spanning tree? (b) How would you generalize this idea? Suppose you are given a graph G and a particular edge {u, v} in the graph. How would you alter Prim’s algorithm to find the minimum spanning tree subject to the condition that {u, v} is in the tree?Write a Java program to find the Adjacency Matrix Representation using Directed Graph. а. Insert new nodes and directed edge between two nodes b. Display the representation
- Q26. * The Adjacency Matrix of the following graph is a ........ matrix. 1 1 2 3 3 0 2 4 1 3 O Symmetric O Asymmetric O Symmetric or Asymmetric O None of themConsider the following graph G. Which vertices of G have degree equal to 2. 0 0 A A B C D E F G t u B V с W D E X TI F y N GTrace 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
- 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…The minimum vertex cover problem is stated as follows: Given an undirected graph G = (V, E) with N vertices and M edges. Find a minimal size subset of vertices X from V such that every edge (u, v) in E is incident on at least one vertex in X. In other words you want to find a minimal subset of vertices that together touch all the edges. For example, the set of vertices X = {a,c} constitutes a minimum vertex cover for the following graph: a---b---c---g d e Formulate the minimum vertex cover problem as a Genetic Algorithm or another form of evolutionary optimization. You may use binary representation, OR any repre- sentation that you think is more appropriate. you should specify: • A fitness function. Give 3 examples of individuals and their fitness values if you are solving the above example. • A set of mutation and/or crossover and/or repair operators. Intelligent operators that are suitable for this particular domain will earn more credit. • A termination criterion for the…Represent the following graph using an edge array, a list of edge objects, an adjacency matrix, an adjacency vertex list, and an adjacency edge list, respectively. 1 3 2