Given the following relations S and U, use ordered pair notation to express the relation U o S. b S с a b U US={Ex: (a, b), (b, c) Hint: Start with a pair of vertices such as (a, b). If there exists some intermediate vertex that a can reach through one arrow in S and that intermediate vertex can reach b through one arrow in U, then (a, b) is in U o S. Otherwise, (a, b) is not in U o S.

Given a graph that is a tree (connected and acyclic). (1) Pick any vertex v. (II) Compute the shortest path from v to every other vertex. Let w be the vertex with the largest shortest path distance. (III) Compute the shortest path from w to every other vertex. Let x be the vertex with the largest shortest path distance. Consider the path p from w to x. Which of the following are true a. p is the longest path in the graph b. p is the shortest path in the graph c. p can be calculated in time linear in the number of edges/vertices a,c a,b a,b,c b.c

Alert dont submit AI generated answer. Write a program that reads a weighted graph and an initial vertex.The program must print on the screen the minimum paths obtained by Dijkstra's algorithm. Input: Receives n, m and s; n is the total number of vertices, m the total number of arcs and s is the initial vertex.Next, m lines, each line with a trio of integers, corresponding to the beginning and end of the arc, followed by the weight of the arc.(Vertices are identified from 0 to n-1.) Output: Prints the shortest paths obtained by Dijkstra's algorithm. Exemple: Input: 5 10 00 1 100 4 51 2 11 4 22 3 43 2 63 0 74 1 34 2 94 3 2 Output: [0, 8, 9, 7, 5][-1, 4, 1, 4, 0]

2. Consider the graph G2(V2, E2) below. 2a. Find the MST of this graph with Kruskal’s algorithm. Draw the MST, and show the table [edge] [w(u, v)] [mark]. 2b. Find the MST of this graph with Prim’s algorithm starting at vertex 'a'. Draw the MST and list the vertices in order you added them to the MST. 2c. Would you get a different MST if you repeat 2b starting at vertex 'e'? Why or why not?

Weighted Graph Applications Demonstration Java Data Structures. Figure 29.23 illustrates a weighted graph with 6 vertices and 8 weighted edges. Simply provide: Minimal Spanning Tree as an illustration or a textual list of edges (in our standard vertex order). Single-Source Shortest Path route from vertex 0 to the other 5 (described as one path/route for each). draw the two solutions and attach the illustration or describe them in text (a list of edges for the one and the vertex to vertex path the other). You can therefore attach proper content files with dot txt, png, jpg or jpeg extensions Be sure the final trees or path lists are clearly visible in your solution. You don't need to show the solution development or progress, just the result.

Computer science question help

Write to code describes how to create the links dataset that represents the input graph. In this particular case, the links represent a directed network. The links dataset has only the nodes identification, which means, the from and to variables. The link weights in the transitive closure problem are irrelevant. In other words, it doesn’t matter the cost or the weight of the links, the algorithm searches for the possible paths to connect the nodes within the input graph. If there is a link or a set of links, no matter the weights, that connects node i to node j, that is the matter.

11. For the given graph below, use the depth-first search algorithm to visit the vertices and write the sequence of the visit. Start from the vertex "A". At any given vertex, you will visit first the unexplored vertex that has least alphabetical order. с G E F Answer the sequence of visiting the vertices: -_

List the vertices of the following graph in the order they will be visited by each of the following Graph traversal methods starting from vertex A: (a) Breadth-First Traversal: (b) Depth-First Traversal: Note: If at any time you have more than possible vertex to visit, you MUST visit them alphabetically. H. lick this link to disnlay it the imano doos not show utomatically hp EGO 814 LA 7614