4. Consider ?3, the graph whose vertex set is ? = {000,001,010,011,100,101,110,111} where two vertices are joined by an edge if and only if they differ in exactly one coordinate. Give a list of three internally disjoint paths that start at 000 and end at 111.
4. Consider ?3, the graph whose vertex set is ? = {000,001,010,011,100,101,110,111} where two vertices are...
question 1 and 2 please, thank you. 1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and the edges between those vertices represent roads. And suppose that you want to start traveling from town A, pass through each town exactly once, and then end at town F. List all the different paths that you could take Hin: For instance, one of the paths is A, B, C, E, D, F. (These...
3. Let G be an undirected graph in which the degree of every vertex is at least k. Show that there exist two vertices s and t with at least k edge-disjoint paths between them. 3. Let G be an undirected graph in which the degree of every vertex is at least k. Show that there exist two vertices s and t with at least k edge-disjoint paths between them.
help :( 5. Let Q. be the graph with vertex set {1,2,..., n}. Two vertices are adjacent if and only if their greatest common divisor is 1. Give the clique number of Q7 and draw a maximum clique of it.
) A vartex cover is n set af vertices for which esch edge has at lesst ane of its vertices in the set. What is the size of the smallest vertex ㏄ver in the Petersen graph? Give an example of such a set Prove that a smaller set does not exist. A dominating sot is a set of vertices for which all other vertices have nt lenst ane neighbar in this set. What is the e of the smallest dominating...
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...
answer question 3 , imagine putting a small cube inside a larger cube and let G be the graph whose vertex set consists of the 8 corners of the small cube and the 8 corners of the larger cube (16 vertices total) and whose edge set consists of the edges in each cube (12 per cube) and the edges joinin corresponding vertices of the two cubes (8 more), for a total of 32 edges. 3. Find a Hamilton Circuit in...
3. Consider the the following graphs for each of the two subproblems. Each subproblem can be answered (or blank) independently of the other ( subject to the 4 total blank for partial credit rule). s MST algorithm on the graph below and left, starting with vertex all work done so far: al (40 points) You are runing Prim' a. You are about to take vertex g out of the min-ehave not done so yet. Show the order that vertices wer...
topic: graph theory Question 4. For n 2, let Gn be the grid graph, whose vertex set is V={(x, y) E Z × Z : 0 < x < n,0
Problem 8. (2+4+4 points each) A bipartite graph G = (V. E) is a graph whose vertices can be partitioned into two (disjoint) sets V1 and V2, such that every edge joins a vertex in V1 with a vertex in V2. This means no edges are within V1 or V2 (or symbolically: Vu, v E V1. {u, u} &E and Vu, v E V2.{u,v} &E). 8(a) Show that the complete graph K, is a bipartite graph. 8(b) Prove that no...
Hello, I'd like someone to help me create these, thanks! 1. Type Vertex Create and document type Vertex. Each vertex v has the following pieces of information. A pointer to a linked list of edges listing all edges that are incident on v. This list is called an adjacency list. A real number indicating v's shortest distance from the start vertex. This number is −1 if the distance is not yet known. A vertex number u. The shortest path from...