Assuming an implementation of a class of undirected graphs, implement a method that detects whether an undirected graph is acyclic. You can look for cycles during either a breadth-first traversal or a depth-first traversal by discovering an edge to a vertex that is not the predecessor and has already been visited. To simplify the problem initially, you can assume that the graph is connected. Then remove this assumption.' Java program

Assuming an implementation of a class of undirected graphs, implement a method that detects whether an undirected graph is acyclic. You can look for cycles during either a breadth-first traversal or a depth-first traversal by discovering an edge to a vertex that is not the predecessor and has already been visited. To simplify the problem initially, you can assume that the graph is connected. Then remove this assumption.' Java program

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 24PE

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write a java program that outputs a walk, trail, path, closed walk, circuit, and cycle of a given directed graph matrix. That matrix is to be hard coded as such... There are 4 vertices in this directed graph. We know that because there are 4 rows and 4 columns. If there is a 1 that means that the vertex on the left (you need to name them) has an arrow edge towards the vertex on the top. If there is a 2 that means there are two directed edges in the same direction going from the left vertex to the vertex on the top. If there is a 0 that means there are no edges from the vertex on the left to the top vertex. 1 2 2 1 2 1 2 1 2 2 1 2 1 1 1 0 - Make sure to program the matrix in to your code. - Output an example of each, make sure they are labeled. (6 outputs ) Example of a directed graph matrix below. The red numbers around the matrix are the vertices. If there is a 0 it means there is no edge from the vertex on the right to the vertex on the top.
Given the weightedGraph class below, implement the Bellman Ford and Dijkstra's algorithms following the instructions in the comments of the screenshots provided. This should be completed in python 3.10 or later please. class WeightedGraph(Graph) : """Weighted graph represented with adjacency lists.""" def __init__(self, v=10, edges=[], weights=[]) : """Initializes a weighted graph with a specified number of vertexes. Keyword arguments: v - number of vertexes edges - any iterable of ordered pairs indicating the edges weights - list of weights, same length as edges list """ super().__init__(v) for i, (u, v) in enumerate(edges): self.add_edge(u, v, weights[i]) def add_edge(self, a, b, w=1) : """Adds an edge to the graph. Keyword arguments: a - first end point b - second end point """ self._adj[a].add(b, w) self._adj[b].add(a, w) def…
In python draw method from the networkx library to draw a graph. Inone of the simple ways to generate a graph, we first define a graph object usingthe Graph method from this library and then can add edges to this object using theadd_edges_from method from a list which specifies edges as vertex pairs as in the
In this question you will explore Graph Colouring algorithms. Given a graph G, we say that G is k-colourable if every vertex of G can be assigned one of k colours so that for every pair u, v of adjacent vertices, u and v are assigned different colours. The chromatic number of a graph G, denoted by χ(G), is the smallest integer k for which graph G is k-colorable. To show that χ(G) = k, you must show that the graph is k-colourable and that the graph is not (k − 1)-colourable. Question: It is NP-complete to determine whether an arbitrary graph has chromatic number k, where k ≥ 3. However, determining whether an arbitrary graph has chromatic number 2 is in P. Given a graph G on n vertices, create an algorithm that will return TRUE if χ(G) = 2 and FALSE if χ(G) 6= 2. Clearly explain how your algorithm works, why it guarantees the correct output, and determine the running time of your algorithm.
Given the graph, please write a java class named Graph.java that: - Inserts a NumberFormat class - Includes an adjacency matrix to represent the graph - Has a constructor that takes a String array of city names as a parameter. - Given two endpoints and the weight of the edge, you will add the edge to the graph. - Build the MST from vertex 0. - Ensure that you utilize prims properly. - Include an overloaded addEdge method and overloaded prims method.
Write a program, in C language, that will do the following: It will show if all the nodes are connected to the graph or not. Given a graph check that it is isomorphic (all nodes and all edges and weights are the same). We are given a graph with non-negative weights (produce them randomly) in which we have randomly colored the edges as red or blue. For each node, find the minimum cost of moving from a source node with the help of a path that has at least one red edge. It will accept a graph and show if it is undirected (if there are directed edges in both directions for all nodes connected to each other).
c++ Given a collection of n edges, each represented by three numbers a, b, and c, you need to: • Output whether we can even make a MST. This requires that our graph can have all nodes connected to one another without cycling and without creating disjoint graphs. • Output the magnitude of the MST, or in other words the value of all edges of the MST added together. If there is no MST possible, output "No". If there is, output "Yes" and continue to the second task. On a new line, output "MST = " + the magnitude of the MST. a is the label of one vertex, b is the label of the other vertex, and c is the size of the edge that connects them. Each value is separated by a space, and each line ends with a endl character. The input will begin with the value of n, followed by a number of combinations of a, b, and c that could be constructed (note: the number of lines are not necessarily equal to or less than n). Make sure your output follows the structure given in the test cases. You MAY use STL…
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. in its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring.", Wikipedia a) Apply your algorithm in the graph below. What is the accuracy ratio? b) Show that the performance ratio of your algorithm can go unbounded above or never at all.
*Discrete Math In the graph above, let ε = {2, 3}, Let G−ε be the graph that is obtained from G by deleting the edge {2,3}. Let G∗ be the graph that is obtain from G − ε by merging 2 and 3 into a single vertex w. (As in the notes, v is adjacent to w in the new if and only if either {2,v} or {3,v is an edge of G.) (a) Draw G − ε and calculate its chromatic polynomial. (b) Give an example of a vertex coloring that is proper for G − ε, but not for G. (c) Explain, in own words, why no coloring can be proper for G but not proper for G − ε. (d) Draw G∗ and calculate its chromatic polynomial. (e) Verify that, for this example,PG(k) = PG−ε(k) − PG∗ (k).
Given a weighted graph class and a PQInt class, please complete the implementation of the Dijkstras algorithm according to the instructions in the screenshot provided. Be done in python 3.10 or later, please class WeightedGraph(Graph) : """Weighted graph represented with adjacency lists.""" def __init__(self, v=10, edges=[], weights=[]) : """Initializes a weighted graph with a specified number of vertexes. Keyword arguments: v - number of vertexes edges - any iterable of ordered pairs indicating the edges weights - list of weights, same length as edges list """ super().__init__(v) for i, (u, v) in enumerate(edges): self.add_edge(u, v, weights[i]) def add_edge(self, a, b, w=1) : """Adds an edge to the graph. Keyword arguments: a - first end point b - second end point """ self._adj[a].add(b, w) self._adj[b].add(a, w) def…
You have a graph G = <V, E>, |V| = n and |E| = m (represented using adjacency matrix you can). Given such a graph and a number k (k <= n). In this graph, a number of k nodes which finds the existence of the subgraph (whether all the elements of k nodes are connected to each other). Develop a brute-force algorithm and write its code in java language ? For example, the graph below is given and your program should send "true" when k = 3 or 4. K = 5 or more your algorithm should send "false" when a large number is entered. Note: No. 2,3,4 and 6 The nodes are all connected to each other. Whichever 3 of these four you take, they all depend on each other. you find a subgraph. This is the case with 4,5 and 6.
6. In Java create an algorithm for an undirected graph with n vertices and m edges that...- Takes as a parameter some integer k- Returns the maximum induced subgraph where each vertex of that subgraph has a degree greater than or equal to k (or returns null if no such subgraph exists)- Operates in O(n + m) time