Given the following vertex set and edge set (assume bidirectional edges): V {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} E={{1,6}, {1, 7}, {2,7}, {3, 6}, {3, 7}, {4,8}, {4, 9}, {5,9}, {5, 10} Is this graph complete? Explain your answer.
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- Draw a graph G containing the following vertices and edges. V(G) = {0, 1, 2, 3, 4, 5, 6} E(G) = { (0, 1), (0, 2), (0, 3), (2, 1), (2, 4), (5, 1), (5, 3)}4. Let G=(V, E) be the following undirected graph: V = {1, 2, 3, 4, 5, 6, 7, 8} E = {(1, 7) (1, 4), (1, 6), (6, 4), (7, 5), (2, 5), (2, 4), (4, 3), (4, 8), (8, 3), (3, 5)}. a. Draw G. b. Is G connected? c. Give the adjacency matrix for the graph G given above. d. Determine whether the graph has a Hamiltonian cycle. If the graph does have a Hamiltonian cycle, specify the nodes of one. If it does not, prove that it does not have one. e. Determine whether the graph has a Euler cycle. If the graph does have a Euler cycle, specify the nodes of one. If it does not, prove that it does not have one.Given the following vertex set and edge set (assume bidirectional edges): V = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} E ={{1,6}, {1, 7}, {2,7}, {3, 6}, {3, 7}, {4,8}, {4, 9}, {5,9}, {5, 10} What is the linked-list based representation of this graph? Assume all edge weights are 1.
- A graph is encoded in the following form graph = [[2,4],[2,3,4],[0,1],[1],[0,1],[7],[9],[5],[0,[6],[12,14],(0,[10],0,[10],[19],[18],[],[16],[15],[23], [23],0.[20,21],[],(0,[27],[26],[],[],[34],[33,34],[],[31],[30,31],[38,39],[37,38,39],[36],[35,36],[35,36], [43],],0,(40],(0,[49],[47,48,49],[46,48,49],[46,47,49],[45,46,47,48]] Which of the following statement best describes the encoding. O A. [2,4] encodes the adjacent vertex 2 and vertex 4. B. The encoding has errors as there are duplication such as [0,1], [0,1] O C. The graph contains a number of vertexes that do not have any adjacent vertices. D. [2,3,4] encodes the vertex 1 has adjacent vertex 2, vertex 3 and vertex 4.Create a graph containing the following edges and display the nodes of a graph in depth first traversal and breadth first traversal. V(G) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} E(G) = {(0, 1), (0, 5), (1, 2), (1, 3), (1, 5), (2, 4), (4, 3), (5, 6), (6, 8), (7, 3), (7, 8), (8, 10), (9, 4), (9, 7), (9, 10)} The input file should consist of the number of vertices in the graph in the first line and the vertices that are adjacent to the vertex in the following lines. Header File #ifndef H_graph #define H_graph #include <iostream> #include <fstream> #include <iomanip> #include "linkedList.h" #include "unorderedLinkedList.h" #include "linkedQueue.h" using namespace std; class graphType { public: bool isEmpty() const; void createGraph(); void clearGraph(); void printGraph() const; void depthFirstTraversal(); void dftAtVertex(int vertex); void breadthFirstTraversal(); graphType(int size = 0); ~graphType(); protected: int maxSize; //maximum number of…Given the following set of vertices (V) and a set of edge (E). Draw the directed graph. • V= {a, b, c} and E = {(a, c), (b, a), (b, b), (b, c), (c, a), (c, c)} V= {a, b, c, d} and E = {{a, a), (a, d), (b, a), (b, d), (c, a), (c, c), (c, d), (d, b), (d, c)}
- Given the following vertex set and edge set (assume bidirectional edges): V {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} E={{1,6}, {1, 7}, {2,7}, {3, 6}, {3, 7}, {4,8}, {4, 9}, {5,9}, {5, 10} What is the adjacency matrix representation of this graph?Draw the graph G = (V, E) with a vertex-set V = {1,2,3,4}and edge-set E = {(1,2),(3,2),(4,3),(1,4),(2,4)}. Find the maximal and minimal degrees and the minimal number of colors needed to color the graph.2. Let G = (V, E) be a directed weighted graph with the vertices V = {A, B, C, D, E, F) and the edges E= {(A, B, 12), (A, D, 17), (B, C, 8), (B, D, 13), (B, E, 15), (B, F, 13), (C, E, 12), (C, F, 25)}, where the third components is the cost. (a) Write down the adjacency list representation the graph G = (V, E).
- 2. Use the following description of an undirected graph and draw the graph: v(Graph1) = { A, B, C, D} E(Graph1) = { (A,B), (A,D), (B,C), (B,D) }Suppose you have the following graph, what is the correct representation of its edges? O F E= {(A,B), (B,D), (C,B), (E,D), (C,E), (F,E)} E= {{A,B}, {B,D}, {C,B}, {E,D}, {C,E}, {F,E}} E= {(A,B), (B,C), (B,D), (C,E), (D,E), (E,F)} E= {(A,B), (B,A), (B,C), (C,B), (B,D), O (D,B), (C,E), (E,C), (D,E), (E,D), (E,F), (F,E)} None of them1. Draw an undirected graph using the following set of edges. A={{1,4},{4,6},{6,5},{5,2},{2,1},{3,1},{2,3},{3,5},{6,3},{3,4}} a. What is the degree of each of the nodes in this graph? b. Is this graph regular?