1) Suppose that a directed graph contains the following edges. Find the strongly connected components. {(h,...
1) Suppose that a directed graph contains the following edges. Find the strongly connected components. {(h, i), (i, j), (j, k), (k, h), (l, m), (m, n), (n, p), (p, l), (f, i), (c, e), (j, b), (k, l), (a, b), (b, c), (c, a), (d, e), (e, f), (f, g), (g, d)}.
a) How many vertices are there in the component having the smallest number of vertices?
b) How many vertices are there in the component having the second smallest number of vertices?
Homework Answers
In the given graph all the vertices are connected therefore there exists only one component with 15 vertices
For both a and b the answer will be 15 only as there is only one component.
Add Answer to:
1) Suppose that a directed graph contains the following edges.
Find the strongly connected components. {(h,...
ignore red marks. Thanks 10. (16) You will compute the strongly connected components of this graph...
ignore red marks. Thanks
10. (16) You will compute the strongly connected components of this graph in three steps. a. STRONGLY-CONNECTED-COMPONENTS (G) (7) Perform a depth-first search on call DFS(G) to compute finishing times w/ for each vertex the following graph. (To make 2 compute GT this easier to grade, everyone call DFS(GT), but in the main loop of DFS, consider the vertices in order of decreasing wf (as computed in line 1) please start with vertex "a" and 4...
In Java: We say that a graph G is strongly-connected if, for every pair of vertices...
In Java: We say that a graph G is strongly-connected if, for every pair of vertices i and j in G, there is a path from i to j. Showhowtotest if G is strongly-connected in O(n + m) time. . Write a method and test it in Main. Explain why it is O(n+m). Graph is directed
1. You will be asked questions about graphs. The graphs are provided formally. To answers the...
1. You will be asked questions about graphs. The graphs are provided formally. To answers the questions, it may help to draw the graphs on a separate sheet. a Consider the graph (V, E), V = {a,b,c,d) and E = {{a,d}, {b,d}, {c, d}}. This graph is directed/undirected This graph is a tree y/n. If yes, the leafs are: This graph is bipartite y/n. If yes, the partitions are: a, d, b, c is/is not a path in this graph....
Can someone help me with (i), the first diagram? 3.4. Run the strongly connected components algorithm...
Can someone help me with (i), the first diagram?
3.4. Run the strongly connected components algorithm on the following directed graphs G. When doing DFS on GR: whenever there is a choice of vertices to explore, always pick the one that is alphabetically first. S. Dasgupta, C.H. Papadimitriou, and UV. Vazirani 107 In each case answer the following questions. (a) In what order are the strongly connected components (SCCs) found? (b) Which are source SCCs and which are sink SCCs?...
Let G be a directed graph on n vertices and maximum possible directed edges; assume that...
Let G be a directed graph on n vertices and maximum possible directed edges; assume that n ≥ 2. (a) How many directed edges are in G? Present such a digraph when n = 3 assuming vertices are 1, 2, and 3. You do not have to present a diagram, if you do not want to; you can simply present the directed edges as a set of ordered pairs. b) Is G, as specified in the problem, reflexive? Justify briefly....
5. The in-degree of a vertex in a directed graph is the number of edges directed...
5. The in-degree of a vertex in a directed graph is the number of edges directed into it. Here is an algorithm for labeling each vertex with its in-degree, given an adjacency-list representation of the graph. for each vertex i: i.indegree = 0 for each vertex i: for each neighbor j of i: j.indegree = j.indegree + 1 Label each line with a big-bound on the time spent at the line over the entire run on the graph. Assume that...
A forest contains 23 vertices and 20 edges. How many connected components does the graph have?
A forest contains 23 vertices and 20 edges. How many connected components does the graph have?
For a directed graph the in-degree of a vertex is the number of edges it has...
For a directed graph the in-degree of a vertex is the number of edges it has coming in to it, and the out- degree is the number of edges it has coming out. (a) Let G[i,j] be the adjacency matrix representation of a directed graph, write pseudocode (in the same detail as the text book) to compute the in-degree and out-degree of every vertex in the Page 1 of 2 CSC 375 Homework 3 Spring 2020 directed graph. Store results...
The number of strongly connected components in graph G is k. By how much can this...
The number of strongly connected components in graph G is k. By how much can this number change if we add a new edge?
Problem 3 (15 points) Consider the graph shown on the right. Find the strongly connected componen...
Problem 3 (15 points) Consider the graph shown on the right. Find the strongly connected components of the graph. For full credit, a) (6 points) Run DFS on the reverse graph, showing the discovery and finish times of each 10 vertex. b) (6 points) Run DFS again, to discover the strongly connected components. What is the 15 order the components are discovered? 12 c) (3 points) Draw the DAG of the components. What is the minimum number of edges that...
ignore red marks. Thanks
10. (16) You will compute the strongly connected components of this graph in three steps. a. STRONGLY-CONNECTED-COMPONENTS (G) (7) Perform a depth-first search on call DFS(G) to compute finishing times w/ for each vertex the following graph. (To make 2 compute GT this easier to grade, everyone call DFS(GT), but in the main loop of DFS, consider the vertices in order of decreasing wf (as computed in line 1) please start with vertex "a" and 4...
1. You will be asked questions about graphs. The graphs are provided formally. To answers the questions, it may help to draw the graphs on a separate sheet. a Consider the graph (V, E), V = {a,b,c,d) and E = {{a,d}, {b,d}, {c, d}}. This graph is directed/undirected This graph is a tree y/n. If yes, the leafs are: This graph is bipartite y/n. If yes, the partitions are: a, d, b, c is/is not a path in this graph....
Can someone help me with (i), the first diagram?
3.4. Run the strongly connected components algorithm on the following directed graphs G. When doing DFS on GR: whenever there is a choice of vertices to explore, always pick the one that is alphabetically first. S. Dasgupta, C.H. Papadimitriou, and UV. Vazirani 107 In each case answer the following questions. (a) In what order are the strongly connected components (SCCs) found? (b) Which are source SCCs and which are sink SCCs?...
5. The in-degree of a vertex in a directed graph is the number of edges directed into it. Here is an algorithm for labeling each vertex with its in-degree, given an adjacency-list representation of the graph. for each vertex i: i.indegree = 0 for each vertex i: for each neighbor j of i: j.indegree = j.indegree + 1 Label each line with a big-bound on the time spent at the line over the entire run on the graph. Assume that...
A forest contains 23 vertices and 20 edges. How many connected components does the graph have?
For a directed graph the in-degree of a vertex is the number of edges it has coming in to it, and the out- degree is the number of edges it has coming out. (a) Let G[i,j] be the adjacency matrix representation of a directed graph, write pseudocode (in the same detail as the text book) to compute the in-degree and out-degree of every vertex in the Page 1 of 2 CSC 375 Homework 3 Spring 2020 directed graph. Store results...
Problem 3 (15 points) Consider the graph shown on the right. Find the strongly connected components of the graph. For full credit, a) (6 points) Run DFS on the reverse graph, showing the discovery and finish times of each 10 vertex. b) (6 points) Run DFS again, to discover the strongly connected components. What is the 15 order the components are discovered? 12 c) (3 points) Draw the DAG of the components. What is the minimum number of edges that...
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