Question #10 please (a) Make a tree that shows all paths beginning at vertexA. List the paths that terminate at C. Indicate which,if any, are Hamiltonian.(b) Is the graph Hamiltonian? Explain.(c) Which roads should be paved so that one may drivefrom A along paved roads to as many towns as pos-sible at minimal cost? Justify your answer. What isthis minimal cost?10. Solve the Traveling Salesman's Problem for each of thefollowing graphs by making trees that display all Hamil-tonian cycles. (Start at A in each case.)(а) А(b)2530101020\3020204070E90 8050100В1560D11. (a) Given that a tree has 100 vertices of degree 1 and20 of degree 6 and that one-half of the remainingvertices are of degree 4 and the rest of degree 2, de-termine the number of vertices of degree 2.(b) Prove that a tree as specified in (a), except that thenumber of vertices of degree 1 must be less than 80,cannot exist.12. [BB] Suppose P1 and P2 are two paths from a vertex v toanother vertex w in a graph. Prove that the closed walkobtained by following P1 from v to w and then P2 inreverse from w to v contains a cycle.13. [BB] (a) Draw the graphs of all nonisomorphic unla-heled trees with five vertices.

To find- Solve the Travelling Salesma's Problem for each of the following graphs by making trees…

Answered: Question #10 please

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.3: Systems Of Inequalities

Problem 15E

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Q1- What is the minimum distance between points C and F? Q2- Which of the following is a Hamiltonian Circuit for the given graph? Q3- What is the length of the Hamiltonian Circuit described in Q2? Q4- Which vertex in the given graph has the highest degree?
a) List all the odd vertices of the graph.b) According to Euler’s Theorem, does the graph have an Eulerian circuit? Howdo you know?c) According to Euler’s Theorem, does the graph have an Eulerian path? Howdo you know? What is the difference between a Hamiltonian path and an Eulerian path? A person starting in Columbus must-visit Great Falls, Odessa, andBrownsville (although not necessarily in that order), and then return home toColumbus in one car trip. The road mileage between the cities is shown Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each vertex. Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in…
Consider the complete bipartite graph K4,3. a) Does it have a Hamiltonian path? b) Does it have a Hamiltonian cycle? c) What is maximum size of a matching in this graph? d) What is minimum size of a vertex cover in this graph?
Trace the graph below to determine whether or not it is Hamiltonian. If not, find the minimum number of edges to be removed to make it so. Mark the edge/s to be removed, and name one resulting Hamiltonian graph using the given letters.
Discrete Maths Oscar Levin 3rd eddition 4.1.15: Prove that any graph with at least two vertices must have two vertices of the same degree. ps: I'd be so glad if you include every detail of the solution.
Which of the graph/s above contains an Euler Trail? Which of the graph/s above is/are Eulerian? Which of the graph/s above is/are Hamiltonian?
Let x and y be two adjacent vertices in the complete bipartite graph Kn,n, n ≥ 3.Find the number of x-y paths of length 2, of length 3, and of length 4.
If G is a Hamiltonian graph, then G has no cut-vertex. True or false? Justify
The weight or cost of a path in a weighted graph is the sum of edge weights of a path. The shortest path from a vertex s to a vertex t is the least cost path from s to t. Given the graph below, which of the following path from s to t is the shortest path?
Find the minimum number of edges to be removed to make it a hamiltonian graph. Mark the edge/s to be removed, and name one resulting Hamiltonian graph using the given letters.
Route Planning. A city engineer needs to inspect the traffic signs at each streetintersection of a neighborhood. The engineer has drawn a graph to represent theneighborhood, where the edges represent the streets and the vertices correspond tostreet intersections. Would the most efficient route to drive correspond to an Eulercircuit, a Hamiltonian circuit, or neither? (The engineer must return to the starting location when finished.) Explain your answer.
Discrete Maths Oscar Levin 3rd eddition 4.1.16: Suppose G is a connected graph with n > 1 vertices and n − 1 edges. Prove that G has a vertex of degree 1. ps: I'd be so glad if you include every detail of the solution

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