using boruvka's algorithm, draw 6 vertices and 10 edges in such a way that the algorithm runs in O(|V|)
The standard application is to a problem like phone network design. You have a business with several offices; you want to lease phone lines to connect them up with each other; and the phone company charges different amounts of money to connect different pairs of cities. You want a set of lines that connects all your offices with a minimum total cost. It should be a spanning tree, since if a network isn't a tree you can always remove some edges and save money.
A less obvious application is that the minimum spanning tree can be used to approximately solve the traveling salesman problem. A convenient formal way of defining this problem is to find the shortest path that visits each point at least once.
Note that if you have a path visiting all points exactly once, it's a special kind of tree. For instance in the example above, twelve of sixteen spanning trees are actually paths. If you have a path visiting some vertices more than once, you can always drop some edges to get a tree. So in general the MST weight is less than the TSP weight, because it's a minimization over a strictly larger set.
using boruvka's algorithm, draw 6 vertices and 10 edges in such a way that the algorithm...
Discrete Mathematics 6: A: Draw a graph with 5 vertices and the requisite number of edges to show that if four of the vertices have degree 2, it would be impossible for the 5 vertex to have degree 1. Repetition of edges is not permitted. (There may not be two different bridges connecting the same pair of vertices.) B: Draw a graph with 4 vertices and determine the largest number of edges the graph can have, assuming repetition of edges...
Consider the following weighted, directed graph G. There are 7 vertices and 10 edges. The edge list E is as follows:The Bellman-Ford algorithm makes |V|-1 = 7-1 = 6 passes through the edge list E. Each pass relaxes the edges in the order they appear in the edge list. As with Dijkstra's algorithm, we record the current best known cost D[V] to reach each vertex V from the start vertex S. Initially D[A]=0 and D[V]=+oo for all the other vertices...
2 (a) Draw the graphs K5,2 and K5,3 using the standard arrangement. For example, K5,2 should have a row of 5 vertices above a row of 2 vertices, and the edges connect each vertex in the top row to each vertex in the bottom row. (b) Draw K5,2 as a plane graph, i.e., with no edges crossing. (c) Complete the following table, recalling E is the number of edges in a graph and V is the number of vertices. (Strictly...
6. (4pts) Draw a simple graph with nine edges and all vertices of degree 3. (this is possible)
Most Edges. Prove that if a graph with n vertices has chromatic number n, then the graph has n(n-1) edges. Divide. Let V = {1, 2, ..., 10} and E = {(x, y) : x, y € V, x + y, , and a divides y}. Draw the directed graph with vertices V and directed edges E.
Draw a graph with 5 vertices, ten edges and no cycles
How much work must Kruskal's MST algorithm do before it starts choosing edges for its MST? Assume the undirected graph has n vertices and m edges. Explain the necessary preliminary work and its big-O cost if done efficiently What are the best case and worst case for Kruskal's MST algorithm with parameters n and/or m? Explain your answer. How much work must Kruskal's MST algorithm do before it starts choosing edges for its MST? Assume the undirected graph has n...
Consider the problem of finding the shortest paths in a weighted directed graph using Dijkstra's algorithm. Denote the set of vertices as V, the number of vertices as |V|, the set of edges as E, and the number of edges as |E|. Answer the following questions.Below is a pseudo-code of the algorithm that computes the length c[v] of the shortest path from the start node s to each node v. Answer code to fill in the blank _______ .
The weights of edges in a graph are shown in the table above. Apply the sorted edges algorithm to the graph. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDEFA
Can you draw the tree diagram for this please 12. Let T be a tree with 8 edges that has exactl 5 vertices of degree 1Prove that if v is a vertex of maximum degree in T, then 3 < deg(v) < 5 12. Let T be a tree with 8 edges that has exactl 5 vertices of degree 1Prove that if v is a vertex of maximum degree in T, then 3