The number of strongly connected components in graph G is k. By how much can this number change if we add a new edge?
The number of strongly connected components in graph G is k. By how much can this...
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...
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?...
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...
Question 2 Show the strongly connected components of the graph below. Mark the edges that comprise the strongly connected components.
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...
(A) Consider the following algorithm for computing a topological sort of a DAG G: add the vertices to an initially empty list in non-decreasing order of their indegrees. Either argue that the algorithm correctly computes a topological sort of G, or provide an example on which the algorithm fails. (B) Can the number of strongly connected components of a graph decrease if a new edge is added? Why or why not? Can it increase? Why or why not? (C) What...
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
10. Graphs (2 points) Determine the following for the graph G: a) List the strongly connected components in G: b) Give the adjacency matrix representation for this graph. a bcd e f
Data Structures/Automata/Graph Theory Question: Problem 1 Find the strongly connected components of the graph shown on Figure1 Figure 1:
The graph G shown below is the union of three connected components G1,G2,G3.(The graph G consists of the three connected components G1, G2 and G3.) (1)what is Chromatic numberχ(G) (2)what is Chromatic polynomialρG(k) (do not expand). (3)what is the number of 6-colorings of G. (No need to simplify the answer.) Gi G2 G3