Given the graph below, list the vertex visitation order of a depth-first search (DFS) beginning at vertex A. [follow alphabetical order] B F A>B>C>E>D>F>H>l>G A>B>C>F>D>E>H>G>I A>B>C>F>D>E>I>H>G O A>B>C>E>F>G>H>I>D O other:
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- 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."Draw a tree with 14 vertices Draw a directed acyclic graph with 6 vertices and 14 edges Suppose that your computer only has enough memory to store 40000 entries. Which best graph data structure(s) – you can choose more than 1 -- should you use to store a simple undirected graph with 200 vertices, 19900 edges, and the existence of edge(u,v) is frequently asked? - Adjacency Matrix - Adjacency List - Edge ListConsider 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
- 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…During the execution of DFS, give the conditions under which there is an edge from a vertex u with color c1 has an edge to a vertex v with color c2. Consider the following color combinations, (c1, c2)= (w,w), (w,g), (g, b) and (b,g).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: (Image taken from the Wikipedia 'Clique Problem' page.) 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 4-clique.…
- 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: (Image taken from the Wikipedia 'Clique Problem' page.) 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 4-clique.…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…"""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…
- Graphs implement the BFS and DFS graph traversal algorithms as a part of the code below (graph.cpp). The code reads in a graph from the sample_edges.txt file (to be put in the same directory as your code), and returns an adjacency list. The adjacency list is a vector, where each element is in turn a vector of (adjacent vertex, edge weight) pairs. Typedef is used to enhance readability. You are to use the adjacency list returned to implement the BFS and DFS algorithms. A header for the helper function is also included to implement DFS recursively. A utility function that prints the queue is provided to help you with the BFS implementation. Note that the BFS an DFS order the vertices are printed could be different from that shown in the test comments. graph.cpp /* Graph read from file, and represnted as adjacency list. To implement DFS and BFS on the graph */ #include <iostream> #include <sstream> #include <fstream> #include <vector> #include…I need help in this question of Graph based on the Screenshot attached URGENT ASAP! True or False a)After executing BFS( G2, A ), the parent of vertex C is vertex A. b)After executing DFS( G2, G ), the parent of vertex D is vertex B. c)After executing DFS( G2, G ), vertex F is a leaf in the DFS-tree. d)After executing DFS( G2, A ), the parent of vertex D is vertex C.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…