Given an undirected connected graph so that every edge belongs to at least one simple cycle...
Given an undirected connected graph so that every edge belongs to at least one simple cycle (a cycle is simple if be vertex appears more than once). Show that we can give a direction to every edge so that the graph will be strongly connected.
Please write time complexity.
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Given an undirected connected graph so that every edge belongs
to at least one simple cycle...
Question 1: Given an undirected connected graph so that every edge belongs to at least one...
Question 1: Given an undirected connected graph so that every edge belongs to at least one simple cycle (a cycle is simple if be vertex appears more than once). Show that we can give a direction to every edge so that the graph will be strongly connected. Question 2: Given a graph G(V, E) a set I is an independent set if for every uv el, u #v, uv & E. A Matching is a collection of edges {ei} so...
3. Let G be an undirected graph in which the degree of every vertex is at least k. Show that ther...
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.
Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears...
Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears at most once) from s to t that goes via v. Create a flow network by making v a source. Add a new vertex Z as a sink. Join s, t with two directed edges of capacity...
3. Graph Connected Components (25 pts) You are given an undirected, unweighted graph that may be...
3. Graph Connected Components (25 pts) You are given an undirected, unweighted graph that may be disconnected i.e. some vertices may not be reachable from other vertices. Every group of mutually reachable vertices forms an island, called a con- nected component. There is no path between vertices in different connected components. If a graph is not disconnected, then its vertices are in a single connected component, which is the entire graph itself. Implement a method using depth-first search that will...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more tha...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
8. For each of the following, either draw a undirected graph satisfying the given criteria or...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
Reachability. You are given a connected undirected graph G = (V, E ) as an adjacency...
Reachability. You are given a connected undirected graph G = (V, E ) as an adjacency list. The graph G might not be connected. You want to fill-in a two-dimensional array R[,] so that R[u,v] is 1 if there is a path from vertex u to vertex v. If no such path exists, then R[u,v] is 0. From this two-dimensional array, you can determine whether vertex u is reachable from vertex v in O(1) time for any pair of vertices...
3, (30 points) Given a directed graph G - N. E), each edge eEhas weight We, 3, (30 points) Given a directed graph...
3, (30 points) Given a directed graph G - N. E), each edge eEhas weight We, 3, (30 points) Given a directed graph G (V, E), each edgee which can be positive or negative. The zero weight cycle problem is that whether exists a simple cycle (each vertex passes at most once) to make the sum of the weights of each edge in G is exactly equal to 0. Prove that the problem is NP complete.
3, (30 points) Given...
Input a simple undirected weighted graph G with non-negative edge weights (represented by w), and a...
Input a simple undirected weighted graph G with non-negative edge weights (represented by w), and a source node v of G. Output: TDB. D: a vector indexed by the vertices of G. Q: priority queue containing the vertices of G using D[] as key D[v]=0; for (all vertex ut-v) [D[u]-infinity:) while not Q. empty() 11 Q is not empty fu - Q.removein(); // retrieve a vertex of Q with min D value for (all vertex : adjacent to u such...
please help state an equation whicn states à relathn of AnB)and P(AB). 3. Prove each of the following two propositions on an undirected graph. 3.1. Every simple closed path contains a cycle. 3.2....
please help
state an equation whicn states à relathn of AnB)and P(AB). 3. Prove each of the following two propositions on an undirected graph. 3.1. Every simple closed path contains a cycle. 3.2. Evevdeg(v) 2E. 4.1. What is the Euler circuit?
state an equation whicn states à relathn of AnB)and P(AB). 3. Prove each of the following two propositions on an undirected graph. 3.1. Every simple closed path contains a cycle. 3.2. Evevdeg(v) 2E. 4.1. What is the Euler circuit?
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.
3. Graph Connected Components (25 pts) You are given an undirected, unweighted graph that may be disconnected i.e. some vertices may not be reachable from other vertices. Every group of mutually reachable vertices forms an island, called a con- nected component. There is no path between vertices in different connected components. If a graph is not disconnected, then its vertices are in a single connected component, which is the entire graph itself. Implement a method using depth-first search that will...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
3, (30 points) Given a directed graph G - N. E), each edge eEhas weight We, 3, (30 points) Given a directed graph G (V, E), each edgee which can be positive or negative. The zero weight cycle problem is that whether exists a simple cycle (each vertex passes at most once) to make the sum of the weights of each edge in G is exactly equal to 0. Prove that the problem is NP complete.
3, (30 points) Given...
Input a simple undirected weighted graph G with non-negative edge weights (represented by w), and a source node v of G. Output: TDB. D: a vector indexed by the vertices of G. Q: priority queue containing the vertices of G using D[] as key D[v]=0; for (all vertex ut-v) [D[u]-infinity:) while not Q. empty() 11 Q is not empty fu - Q.removein(); // retrieve a vertex of Q with min D value for (all vertex : adjacent to u such...
please help
state an equation whicn states à relathn of AnB)and P(AB). 3. Prove each of the following two propositions on an undirected graph. 3.1. Every simple closed path contains a cycle. 3.2. Evevdeg(v) 2E. 4.1. What is the Euler circuit?
state an equation whicn states à relathn of AnB)and P(AB). 3. Prove each of the following two propositions on an undirected graph. 3.1. Every simple closed path contains a cycle. 3.2. Evevdeg(v) 2E. 4.1. What is the Euler circuit?
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