(b) Label the vertices of the graph given below so that if DFS is run starting at vertex a and the neighbors are considered in alphabetical order, then the resulting DFS tree consists of the edges shown in red.

7. Consider the following graph: A 14 CO D 9 E C 12 10 17 b) What is the weight of the minimum spanning tree? B Apply Kruskal's algorithm to find the minimum spanning tree. Edges are sorted first by length, and in the event of a tie, by name, where the two letters are in alphabetical order. Use makeset (x), find (x), and union (x, y) to determine if there are cycles. a) Circle the edges that are part of the minimum spanning tree. AC, AD, AE, BC, BD, BE, DE c) Draw the tree that results from applying the union-find algorithm for cycle detection. When drawing the tree, put vertices with lower letters in the left subtrees so that all the vertices in a level are sorted alphabetically from left to right

A B. D H Suppose you run the topological sort algorithm on the graph above starting at vertex C. Use the rule that when there is a choice of vertices for the algorithm to visit, it visits them in alphabetic order. Which vertex would end up first in the eventual topologically sorted order? Which would end up being second? Which would end up being third? Which would end up being fourth? Which would end up being fifth? Which would end up being sixth?

Kruskal's minimum spanning tree algorithm is executed on the following graph. Select all edges from edgeList that belong to the minimum spanning tree. edgeList result List AD BC BE CF EF DG EG EH GH D 7 9 G 1 B 5 3 A E H 4 2 6 8 F

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…

2. Consider the graph G2(V2, E2) below. 2a. Find the MST of this graph with Kruskal’s algorithm. Draw the MST, and show the table [edge] [w(u, v)] [mark]. 2b. Find the MST of this graph with Prim’s algorithm starting at vertex 'a'. Draw the MST and list the vertices in order you added them to the MST. 2c. Would you get a different MST if you repeat 2b starting at vertex 'e'? Why or why not?

Weighted Graph Applications Demonstration Java Data Structures. Figure 29.23 illustrates a weighted graph with 6 vertices and 8 weighted edges. Simply provide: Minimal Spanning Tree as an illustration or a textual list of edges (in our standard vertex order). Single-Source Shortest Path route from vertex 0 to the other 5 (described as one path/route for each). draw the two solutions and attach the illustration or describe them in text (a list of edges for the one and the vertex to vertex path the other). You can therefore attach proper content files with dot txt, png, jpg or jpeg extensions  Be sure the final trees or path lists are clearly visible in your solution.  You don't need to show the solution development or progress, just the result.

1. This question is about type of graphs. a. Construct a graph with exactly 5 nodes such that the graph is strongly connected. b. Construct a graph with exactly 5 nodes such that the graph is weakly connected. c. Construct a graph with exactly 5 nodes such that the graph is completely connected. d. Construct a graph with exactly 5 nodes such that the graph is not connected. e. Construct a graph with exactly 5 nodes such that the graph is not a simple graph.

Please provide all the spanning trees possible from the graph below:

Give an example of a graph that has all 3 of the following properties. (Note that you need to give a single graph as the answer.) (i)  It is connected (ii)  It has one articulation point. (iii)  The graph needs at least 4 colors for a valid vertex coloring (iv)  The graph does not have a 4-clique (that is, a clique of 4 vertices) as a subgraph.