Kindly answer the attached question using python and without using any of its libraries
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Kindly answer the attached question using python and without using any of its libraries
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- 4-Clique Problem The clique problem is to find cliques in a graph. A clique is a set of vertices that are all adjacent - connected - to each other. A 4-clique is a set of 4 vertices that are all connected to each other. So in this example of the 4-Clique Problem, we have a 7-vertex graph. A brute-force algorithm has searched every possible combination of 4 vertices and found a set that forms a clique: https://en.wikipedia.org/wiki/Clique_problem You should read the Wikipedia page for the Clique Problem (and then read wider if need be) if you need to understand more about it. Note that the Clique Problem is NP-Complete and therefore when the graph size is large a deterministic search is impractical. That makes it an ideal candidate for an evolutionary search. For this assignment you must suppose that you have been tasked to implement the 4-clique problem as an evolutionary algorithm for any graph with any number of vertices (an n-vertex graph). The algorithm succeeds if it finds a…Graph ColoringNote that χ(G) denotes the chromatic number of graph G, Kndenotes a complete graph on n vertices, and Km,n denotes the complete bipartite graph inwhich the sets that bipartition the vertices have cardinalities m and n, respectively. (c) Compute χ(K3,3). Justify your answer with complete details and complete sentences. (d) For n, m ∈ N, compute χ(Km,n). Do not justify your work. (e) Give an example of a graph G whose chromatic number is 3, but that contains no K3 as a subgraph"""1.In a directed graph, a strongly connected component is a set of vertices suchthat for any pairs of vertices u and v there exists a path (u-...-v) thatconnects them. A graph is strongly connected if it is a single stronglyconnected component.""" from collections import defaultdict class Graph: """ A directed graph where edges are one-way (a two-way edge can be represented by using two edges). """ def __init__(self,vertex_count): """ Create a new graph with vertex_count vertices. """ self.vertex_count = vertex_count self.graph = defaultdict(list) def add_edge(self,source,target): """ Add an edge going from source to target """ self.graph[source].append(target) def dfs(self): """ Determine if all nodes are reachable from node 0 """ visited = [False] * self.vertex_count self.dfs_util(0,visited) if visited == [True]*self.vertex_count: return True…
- WRITE A PROGRAM IN C++ BFS traverses the graph in a concentric fashion, visiting all vertices that are near to a starting vertex, then all unvisited vertices two edges away from it, and so on, until all vertices in the same linked component as the initial vertex are visited. BFS utilises queue in place of a stack. Input graph as Adjacency Matrix Constraints NA Output Format space separated nodes, which are rechable Sample Input 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 Sample Output 0 2 3 4Write a program (WAP) to create an undirected graph using adjacency matrix representation.Number of nodes and edges should be taken from the user. After creating the graph, performfollowing operations: (6 Marks)(i) Search a node. Take the node number from the user. If the node is found then print its associatededges.(ii) Insert a node in the graph.(iii) Insert an edge in the graph. Take the node numbers from the user between which the edge is tobe inserted.(iv) Delete a node from the graph. Take the node number to be deleted from the user.(v) Apply DFS on the graph and print the graph traversal.(vi) Apply BFS on the graph and print the graph traversal.Write a program (WAP) to create an undirected graph using adjacency matrix representation.Number of nodes and edges should be taken from the user. After creating the graph, performfollowing operations: (i) Search a node. Take the node number from the user. If the node is found then print its associatededges.(ii) Insert a node in the graph.(iii) Insert an edge in the graph. Take the node numbers from the user between which the edge is tobe inserted.(iv) Delete a node from the graph. Take the node number to be deleted from the user.(v) Apply DFS on the graph and print the graph traversal.(vi) Apply BFS on the graph and print the graph traversal.Solve the above problem using adjacency list representation.
- class Dijkstra(): """ A fully connected directed graph with edge weights """ def __init__(self, vertex_count): self.vertex_count = vertex_count self.graph = [[0 for _ in range(vertex_count)] for _ in range(vertex_count)] def min_distance(self, dist, min_dist_set): """ Find the vertex that is closest to the visited set """ min_dist = float("inf") for target in range(self.vertex_count): if min_dist_set[target]: continue if dist[target] < min_dist: min_dist = dist[target] min_index = target return min_index def dijkstra(self, src): """ Given a node, returns the shortest distance to every other node """ dist = [float("inf")] * self.vertex_count dist[src] = 0 min_dist_set = [False] * self.vertex_count for _ in range(self.vertex_count): #minimum distance vertex that is not processed…Complete code asap. class Dijkstra(): """ A fully connected directed graph with edge weights """ def __init__(self, vertex_count): self.vertex_count = vertex_count self.graph = [[0 for _ in range(vertex_count)] for _ in range(vertex_count)] def min_distance(self, dist, min_dist_set): """ Find the vertex that is closest to the visited set """ min_dist = float("inf") for target in range(self.vertex_count): if min_dist_set[target]: continue if dist[target] < min_dist: min_dist = dist[target] min_index = target return min_index def dijkstra(self, src): """ Given a node, returns the shortest distance to every other node """ dist = [float("inf")] * self.vertex_count dist[src] = 0 min_dist_set = [False] * self.vertex_count for _ in range(self.vertex_count): #minimum distance vertex that…''In graph theory, a component, sometimes called a connected component,of an undirected graph is a subgraph in which anytwo vertices are connected to each other by paths.Example: 1 3------------7 | | 2--------4 | | | | output = 2 6--------5''' # Code is Here def dfs(source,visited,adjacency_list): ''' Function that performs DFS ''' visited[source] = True for child in adjacency_list[source]: if not visited[child]: dfs(child,visited,adjacency_list) def count_components(adjacency_list,size): ''' Function that counts the Connected components on bases of DFS. return type : int ''' count = 0 visited = [False]*(size+1) for i in range(1,size+1): if not visited[i]: dfs(i,visited,adjacency_list) count+=1 return count def main(): """ Example application """ node_count,edge_count = map(int, input("Enter the Number of Nodes and Edges…
- JAVA: Write a program that takes a graph representing a map between cities and use Dijkstra's Algorithm to find the shortest path given a start and an end vertex. in java 1- Please comment the codes.When a vertex Q is connected by an edge to a vertex K, what is the term for the relationship between Q and K? *a) Q and K are "insecure."b) Q and K are "incident."c) Q and K are "adjacent."d) Q and K are "isolated."Consider the following graph. If we run breadth first search on this graph starting at any vertex, which one of the following is a possible order for visiting the nodes? NQMPOR QMNPOR MNOPQR QMNPRO Assume the following adjacency list for a graph. After you draw the graph, what is the path to reach D from A. Vertex Edges A --------> B, C B --------> C C --------> B, E D --------> B E --------> B, D Both (B) and (C) A->B->C->E->D A->B->C->D A->C->E->D