1. Determine whether or not the graph shown is Hamiltonian. Determine also whether or not the graph has a Hamiltonian path. In each case, either number the vertices so as to indicate a Hamiltonian cycle or path or explain why no such cycle or path exists.

Q: Suppose a graph G has the following Hamiltonian Cycle: BAGDFHEJKXB a. How many vertices does G have?…

A: A Hamiltonian cycle is a closed loop on a graph where every vertex is visited exactly once. A loop…

Q: Refer to the graph in problem 6 above. a f e An Euler Path exists between A and C. True False O More…

A: Remark: Euler path: An Euler path in a graph is a path that passes through every edges of a graph…

Q: . Let G be the graph below. (a) Does G has the Hamiltonian path? (b) Does G has the Hamiltonian…

A:

Q: 4. Highlight a Hamiltonian cycle, if possible, in each of the following graphs, or state that no…

A: To find- Highlight a Hamiltonian cycle, if possible, in each of the following graphs, or state that…

Q: Let x and y be two adjacent vertices in the complete bipartite graph Kn,n,     n ≥ 3. Find the…

A:

Q: (4) The questions on this page refer to the graph shown here: • Specify any trail/tour/cycle as a…

A: The solution to the given question is explained below.

Q: Determine and explain whether or not the following graph is Hamiltonian:

A: We need to check whether the given graph is a Hamiltonian graph or not.

Q: Based on the graph below, which of the following statements is FALSE? B E А. The graph is…

A: To find - Based on the graph below, which of the following statements is False ? The graph is…

Q: Draw a simple graph (or argue why one cannot exist) that (a) has 6 vertices, 12 edges, and is…

A: (a)Such a graph is not possible as we can seeK3 has 3 vertices 3 edgesK2 has 2 vertices and 1 edgeK4…

Q: 18. Which of the following is false? A) Hamiltonian cycle can be converted to a Hamiltonian path by…

A: We know that ,  A Hamiltonian path is a graph path between vertices of a graph that visits each…

Q: Prove that connecting two nodes u and v in a graph G by a new edge creates a new cycle if and only…

A: Given, Connecting two nodes u and v in a graph G by a new edge creates a new cycle such that if and…

Q: Consider the following graph G with five vertices a, b, c, d, and e: a b d e Select all true…

A: Connected graph A graph is said to be connected if there is a  path between every pain of vertices…

Q: 1. Determine and explain whether or not the following graph is Hamiltonian:

A: 1. If there exists a closed walk in the connected graph that visits every vertex of the graph…

Q: A graph with four vertices is Hamiltonian if each vertex has a degree of two. True O False

A:

Q: A. Explain why the graph below is not Hamiltonian. G: to

A: Hamiltonian Graph: A Graph G(V,E) is said to be Hamiltonian if there exists a closed walk in the…

Q: Question 4 What is the minimum number of duplicated edges needed to create a good Eulerization for…

A: An Eulerian graph is a graph in which there is an Euler circuit. That is we can get a circuit that…

Q: - In Exercises 27 and 28, count the number of vertices, edges, and faces in the graph, and then…

A:

Q: Find a Hamiltonian circuit in the following graph. (There is more than one possible answer.) Either…

A: A Hamiltonian circuit is a circuit that visits every vertex once except the first vertex which is…

Q: Does the following graph have a Hamiltonian circuit? b This graph has the following Hamiltonian…

A: The main objective is to determine the Hamiltonian circuit of the given graph.

Q: A number N is said to be a Hamilton realizable if, given a weighted graph, we can find a Hamiltonian…

A: We can first find out the Hamiltonian Cycles that are possible in this graph and find the weight of…

Q: 7. (refer to the graph below) Which graph contains Hamiltonian Circuit? For those that don’t give an…

A: The Hamiltonian circuits of the given graphs are determined as shown below.

Q: 1.(a)Determine with proof whether the following graph G is Hamiltonian. (b)Give a minimal set of…

A: The graph given is as follows:

Q: ) Determine with justification which of the following statements is true: • Gis an Eulerian graph…

A: Ans (4)  Eulerian graph consist 2 properties              Euler path => Edges will not repeat in…

Q: If a graph G has a subgraph H with 1. ĮV(H)| = |V(G)| 2. H is connected 3. Je(H)| = |V(H)| %3D 4. Vu…

A:

Q: 3. A labeled Ks graph with labeled edges appears below. Which edge permutation is induced by the…

A: Solution:

Q: Consider the following graph. Label all the vertices and edges. Determine whether the graph has a…

A: Consider the given graph and label it.

Q: C D A E F Find any Hamiltonian circuit on the graph above. Give your answer as a list of vertices,…

A:

Q: Answer the following questions. a. If a graph is Hamiltonian, is it necessarily Eulerian as well? If…

A: Hamilonian GraphA Hamiltonian graph is one which has a Hamiltonian cycle.A Hamiltonian cycle is a…

Q: QUESTION 13 Total number of hamiltonian circuits of the complete graph K is 12 circuits 48 circuits…

A:

Q: If G is a Hamiltonian graph, then G has no cut-vertex. True or false? Justify

A: In order to find the solution of the given question, we will use the concept of Hamiltonian graph…

Q: What is the Hamiltonian circuit in the given graph below? B. F D. B- F C- E - D - A – B А - D - E -…

A: For the Hamiltonian circuit, the vertex of the graph is visited exactly once. Since, it is a…

Q: Which of the following is false? A.) Hamiltonian cycle can be converted to a Hamiltonian path by…

A: Option (B)  is FALSE . Because there exist graph that contains Hamiltonian path but does not contain…

Q: Trace the graph below to determine whether or not it is Hamiltonian. If not, find the minimum number…

A: Hamiltonian graph:

Q: 3) What is the adjacency matrix Ac for the following graph G based on the order of the vertices a,…

A: Note: Since you have asked multiple independent questions, we are only allowed to answer one. Thank…

Q: The graph below has alan * A B F D Euler Tour Hamiltonian Cycle Both Neither

A: This graph is both Euler Tour and Hamiltonian Cycle. Because for Euler Tour we can draw the given…

Q: 7. Find the Euler circuit Euler trail for the graphs below. Also find the Hamiltonian circuit.

A: Graphs are given , we have to find Euler circuit and Hamiltonian circuit.

Q: 3. а) Define the following terms as used in graph theory: i) regular graph ii) simple circuit 1 21 1…

A: The solution is given as follows

Q: 7. a) How many different paths of length 2 are there in the undirected graph G in Fig. 11.43? b) Let…

A: Path : A path in a graph is a finite or infinite sequence of edges which joins a sequence of…

Q: The graph with two vertices is Hamiltonian. True False

A: Definition - A graph is Hamiltonian connected if for every pair of vertices there is a Hamiltonian…

Q: a. Show that K5,6 has a path containing all vertices in the graph. b. Explain why K5,6 is not…

A: Hamiltonian graph - A connected graph G is called Hamiltonian graph if there is a cycle which…

Q: 3. Provide a graph (aside from the examples in our class discussion) that has an Eulerian path.…

A: Solution:

Q: a e d b C

A:

Q: If a graph G has a subgraph H with 1. [V(H)| = |V(G)| 2. H is connected 3. Je(H)| = |V(H)| %3D 4. Vu…

A: The necessary condition for a graph to be Hamiltonian circuit is that the graph must be connected,…

Q: The graph below has alan * A В E F D O Euler Tour Hamiltonian Cycle Both O Neither

A:

Q: Refer to the graph and choose the best answer: * a) Neither a Hamiltonian path nor Hamiltonian cycle…

A:

Q: Question 3 Draw a complete graph with five vertices labeled A, B, C, D, and E. a. b. Find one…

A:

Q: Exercise #3," Which graph is Eulerian? Which graph is not Eulerian but contains an Eulerian path?…

A: We Know that  An Eulerian  path is a trail in a finite graph that visits every edge exactly once…

Q: a. If a graph is Hamiltonian, is it necessarily Eulerian as well? If yes, explain why. If no,…

A:

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.