5) Let G be the Petersen Graph. a)Delete one edge and one vertex . Use SAGE Program. b) Let e be an edge and v be a vertex then perform the G-e-v Use SAGE Program.

Q: 2. a) In the following graph, apply Depth First Search algorithm to find the Strongly Connected…

A: Answer as given below:

Q: 1. where do you insert the graph into dijkstras algorithm ? 2. how do you insert the graph into…

A: In this question we have to understand where and how the Dijkstra's algorithm is used and graph is…

Q: A graph is finite if O (b) It vertex set is infinite. (c) Both of it is vertex set and it is edge…

A: As per the question , the graph is finite if

Q: c) Find a Hamiltonian cycle starting at vertex A. Draw the Hamiltonian cycle on the graph and list…

A: Given that, A Hamiltonian cycle is a simple cycle that traverse all the vertices in the graph.…

Q: B H) F Fig. 1

A: Here in this question we have given a graph.and we have akes to apply DFS on this graph and find…

Q: iii) Determine if the graph below is flattenable and determine its chromatic number. Note: Justify…

A: Answer: We have done graph coloring and and also find the chromatic number so we will see in the…

Q: Q6. (.. ») Apply the backtracking algorithm for the 3-coloring problem on the graph below,…

A: The Answer is in step-2.

Q: 6. Run Dijkstra's algorithm on the directed graph in Figure 4, using vertex 1 as the source. Show…

A: 6. The source vertex given is vertex 1. Initialization :  For every vertex, there are 2 parameters…

Q: (Pre- and Post- Order Correspondence, Suppose that for a graph G you are given the list of the…

A: Pre- and Post- Order Correspondence, Suppose that for a graph G you are given the list of the…

Q: a d b a) Give the vertex set of the G. b) Give the set of edge of G. c) Find the degree of each of…

A: In this question we have been given with the graph and we have to answer for the graph theory…

Q: Take 8 different capital letters and place them into the vertices of a graph.     Show:…

A: “Since you have posted a question with multiple sub-parts, we will solve first two subparts for you.…

Q: (1)In a graph, the sum of the degrees of all vertices is equal to () times the number of edges of…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Apply the proper Theorems and formulas to answer the following questions using the correct…

A: 1) yes this is connected graph as there are not any vertices which cannot be reachable from any…

Q: Python code to simply calls this method to find the centrality values for the graph of Fig. 10.6 and…

A: One strategy is to test every possible outcome. We go through the array after sorting it by height.…

Q: 2. Given any number of vertices n, how many edges in terms of n are needed to make a wheel graph?

A: A wheel graph in general has n+1 vertices. The n vertices are of degree 3 and the central vertex is…

Q: a) Given graph A and graph B. Is there Eulerian path and why? A A B (C) B D Graph A Graph B b)…

A: 4a) Both the graphs have the Eulerian path. Graph A can have the Eulerian path as -> A B D C(as…

Q: II. Solve the following problems applying the concept of Eulerian and Hamiltonian Graphs. Discuss…

A: The question is related to graph theory and finding route which will traverse all of the streets or…

Q: Discuss the graph operations: 1. Element checking in the graph 2. Graph traversal 3. Adding of…

A: A graph operation refers to any action or procedure performed on a graph data structure. It…

Q: The number of spanning trees from the following graph are a

A: The answer is given in the steps below.

Q: B. (20 points) Consider the following graph a. Compute Compute the topic-sensitive PageRank for the…

A:

Q: 1) Execute the dijsktra algorithm on the following graph, with single-source A. (ON NEXT PAGE) 1 В…

A: Given fiigure, Initially,   A B C D E d 0 ∞ ∞ ∞ ∞ π - - - - -

Q: A graph without multiple edges and loops is called a graph. (simple graph, mixed graph)

A: Actually, given question regarding graph.

Q: D E B G A In the graph above, assume Floyd-Warshall is run on vertices in alphabetic order, i.e. A…

A: Floyd-Warshall  Algorithm is for solving the All pairs shortest path problem with positive and…

Q: (a) All of the following four statements are false. Provide a counterexample for each one. i. If a…

A:

Q: (a) 10 5 (b) 10 3 (11 7

A: - We need to get the path from vertex 1 to vertex  9.

Q: Consider the two-player game, Nim, as discussed in the lecture. (i.e. The two players take turns to…

A:

Q: 3. Given any number of vertices n, how many edges in terms of n are needed to make a complete graph…

A:

Q: ximum number of edges that can exist in an undirected graph? Why? Explain.

A: As per guidelines, answering 1st 3 subparts. Repost other subparts.

Q: . Apply Prim's algorithm to the following graph. 5 a 7 с 2 4 e 4 3 5 b 6 d

A: Prim’s algorithm is a greedy algorithm that is used for finding the minimum spanning tree of a…

Q: Q1) Graph the parabola (y = X +4x + 3) and label the Vertex, axis, and intercepts.

A:

Q: Case Study 5 0 2 1 8 Figure 2 4 5 Problem: Most graph algorithms involve visiting each vertex in a…

A: - BFS stands for Breadth First Search which is a graph traversal algorithm that uses queue to…

Q: 3 A B 6 C 1 2, 1 3 5 H Figure 2 i) You are given a network of nodes as in Figure 2, starting from…

A: Breadth first search tree is the traversing the nodes level by level. Given graph contains 8 nodes…

Q: Q2) a) Show that K is not planar graph. Use Euler formula. b) A connected planar graph has nine…

A: Given,a) Show that K5 is not planar graph. Use Euler formula. b) A connected planar graph has nine…

Q: Apply improved Dijkstra’s algorithm to the following graph to find the shortest path from A to every…

A: Dijkstra’s algorithm An algorithm that is used for finding the shortest distance, or path, from…