Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 34.1, Problem 2E
Program Plan Intro
To define the problem of finding the longest simple cycle in an undirected graph. To give a related problem and to define the language corresponding to decision problem.
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Draw a simple, connected, weighted graph with 8 vertices and 16 edges, each with unique edge weights. Identify one vertex as a “start” vertex and illustrate a running of Dijkstra’s algorithm on this graph.
Problem R-14.23 in the photo
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Question 2: Draw a simple undirected graph G that has 11 vertices, 7 edges.
Refer to the undirected graph provided below:
B
G
What is the maximum length of a path in the graph? Give an example of
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What is the maximum length of a cycle in the graph? Give an examnple of
a cycle of that length.
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but not a path.
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сircuit.
Give an example of a circuit of length zero in the graph.
Chapter 34 Solutions
Introduction to Algorithms
Ch. 34.1 - Prob. 1ECh. 34.1 - Prob. 2ECh. 34.1 - Prob. 3ECh. 34.1 - Prob. 4ECh. 34.1 - Prob. 5ECh. 34.1 - Prob. 6ECh. 34.2 - Prob. 1ECh. 34.2 - Prob. 2ECh. 34.2 - Prob. 3ECh. 34.2 - Prob. 4E
Ch. 34.2 - Prob. 5ECh. 34.2 - Prob. 6ECh. 34.2 - Prob. 7ECh. 34.2 - Prob. 8ECh. 34.2 - Prob. 9ECh. 34.2 - Prob. 10ECh. 34.2 - Prob. 11ECh. 34.3 - Prob. 1ECh. 34.3 - Prob. 2ECh. 34.3 - Prob. 3ECh. 34.3 - Prob. 4ECh. 34.3 - Prob. 5ECh. 34.3 - Prob. 6ECh. 34.3 - Prob. 7ECh. 34.3 - Prob. 8ECh. 34.4 - Prob. 1ECh. 34.4 - Prob. 2ECh. 34.4 - Prob. 3ECh. 34.4 - Prob. 4ECh. 34.4 - Prob. 5ECh. 34.4 - Prob. 6ECh. 34.4 - Prob. 7ECh. 34.5 - Prob. 1ECh. 34.5 - Prob. 2ECh. 34.5 - Prob. 3ECh. 34.5 - Prob. 4ECh. 34.5 - Prob. 5ECh. 34.5 - Prob. 6ECh. 34.5 - Prob. 7ECh. 34.5 - Prob. 8ECh. 34 - Prob. 1PCh. 34 - Prob. 2PCh. 34 - Prob. 3PCh. 34 - Prob. 4P
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- Let G be simple graph containing a simple circuit C on n vertices. (Check the definitions of simple circuit and simple graph.) Show by induction that for n > 3, the circuit C contains n edges.arrow_forward. Prove the following.(Note: Provide each an illustration for verification of results)Let H be a spanning subgraph of a graph G.i. If H is Eulerian, then G is Eulerian.ii. If H is Hamiltonian, then G is Hamiltonianarrow_forwardSUBJECT: GRAPH ALGORITHMS Prove that if v0 and v1 are distinct vertices of a graph G = (V,E) and a path exists in G from v0 to v1 , then there is a simple path in G from v0 to v1 .arrow_forward
- Suppose you have a graph G with 6 vertices and 7 edges, and you are given the following information: The degree of vertex 1 is 3. The degree of vertex 2 is 4. The degree of vertex 3 is 2. The degree of vertex 4 is 3. The degree of vertex 5 is 2. The degree of vertex 6 is 2. What is the minimum possible number of cycles in the graph G?arrow_forward3) The graph k-coloring problem is stated as follows: Given an undirected graph G= (V,E) with N vertices and M edges and an integer k. Assign to each vertex v in V a color c(v) such that 1arrow_forwardSay that a graph G has a path of length three if there exist distinct vertices u, v, w, t with edges (u, v), (v, w), (w, t). Show that a graph G with 99 vertices and no path of length three has at most 99 edges.arrow_forwardDraw the following:a. Complete graph with 4 vertices b. Cycle with 3 vertices c. Simple graph with 2 vertices d. simple disconnected graph with 3 vertices e. graph that is not simple. For each of the graphs shown below, determine if it is Hamiltonian and/or Eulerian. If the graph is Hamiltonian, find a Hamilton cycle; if the graph is Eulerian, find an Euler tour.arrow_forwardINPUT: A graph G, a non-negative integer k ≥ 0, and a boolean formula F in CNF. OUTPUT: “Yes” if and only if either G has an independent set of size k or if the boolean formula F is satisfiable. Prove that this problem is NP-Complete.arrow_forwardHow many edges does a graph have if its degree sequence is 2, 4, 4, 5, 3?A. Draw a graph with the above listed sequence.B. Is it possible to draw an Euler Circuit with such a sequence of vertex degrees?Is it possible to draw an Euler Path? If yes, to either of these questions, draw the a graph that supports your answer.arrow_forwarda 2. Consider the graph G drawn below. d b e a) Give the vertex set of the G. Give the set of edge of G. b) c) Find the degree of each of the vertices of the graph G. d) Add the degrees of all the vertices of the graph G and compare that sum to the number of edges in G, what do you find? e) Give a path of length 1, of length 2, and of length 3 in G. f) Find the longest path you can in G? h (Remember that you cannot repeat vertices).arrow_forwardIn a planar drawing of a graph, each face is bounded by a circuit. Make a planar drawing of a graph that is equivalent to the graph shown, in which faces are bordered by the same circuits as the given graph but where the face bordered by A – B – C – G – F – A is in the infinite face.arrow_forwardFloyd warshall algorithm java program. Find the shortest paths between all vertices in a graph using dynamic programming. The matrix and number of vertices as the input(using the scanner), and the shortest path matrix as the output.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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