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)}

Draw the graph based on its representation. (a) V = {a, b, c, d} E = {{a, b}, {a, d}, {b, c}, {b, d}, {c, d}} (b) a bd b a c le C b|d d. a o e b |d (c) 0 1 1 0 0 10 0 0 1 10 0 1 1 0 0 10 1 0 1 110

consider the undirected graph

In the following graph, find all the shortest paths from vertex "a" to all the other vertices.

Consider the following graph: What is the chromatic number of this graph?

Find the number of connected components for the following graph.

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…

Draw the undirected graph that is represented by the following:  vertices: 1, 2, 3, 4, 5, 6, 7 edges: (1, 2), (1, 4), (2, 3), (2, 4), (3, 7), (4, 7), (4, 6), (5, 6), (5, 7), (6, 7)

A simple directed graph with vertices A,B,C,D,E,F,G has adjacency matrix

Give an example of a graph that has all of the following properties. (Give a single graph as the answer.) (i) It does not have any articulation point. (ii) It does not have a Hamiltonian cycle (iii) It does not have a valid vertex coloring with only 2 colors.