The graph below is used for problems 10 and 11.ABa) BDb) ABc) CDd) BC6Dc) 45d) none of these81512272011E10. Using the Greedy Algorithm to find an approximate solution to the traveling salesmanproblem for a circuit starting at vertex B, the first edge chosen when constructing the circuitis12. A solution to the "traveling salesman problem" isa) an Eulerian circuit of minimum weight.b) a Hamiltonian circuit of minimum weight.c) a spanning tree of minimum weight.d) all of the above.16с11. After applying the Greedy Algorithm, the total weight of the circuit constructed isa) 23b) 48

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Answered: The graph below is used for problems 10…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Euler's Formula F + V = E+1 applies to any two-dimensional network where F is the number of regions formed by V vertices linked by E edges (or paths). Verify Euler's Formula for the network to the right. Choose the correct answer below. ? O A. 1+4 = 4 + 1 5 = 5 В. 2+5 = 6+1 7 = 7 ? C. 1+5 = 5+ 1 6 = 6 ? O D. 2+4 = 5+1 6 = 6
2. Show that the graphs formed by deleting one edge from Kş and K33 are planar.
3. A company makes unusually shaped imitation dimonds. One dimond had 12 faces and 19 edges. How many vertices did the diamond have? Use Euler's Formula to check your answer.
A and B can do a piece of work in 12 days; B and C can do it in 15 days while C and A can finish it in 20 days. In how many days will A,B,C finish it, working togeteher? In hpw many days will each one of them finish it, working alone?
In 1.54Pathfinding, we consider the a path with fixed start and end points on a grid. Thepaths may move right and up on the grid only. Suppose we have points A = (a1, a2) B = (b1, b2) C = (c1, c2) D = (d1, d2)where a1 < b1 < c1 < d1 and a2 < b2 < c2 < d2.(a) Write an expression for the probability that a random path from A to D will pass throughboth B and C.(b) Write an expression for the probability that a random path from A to D will pass throughB, but not C.(c) Write an expression for the probability that a random path from A to D will pass throughneither B nor C.(d) Find the probability a path from (0, 0) passes through (9, 9), but not (5, 5) or (7, 7).
6. a. Assume that graph G has 6 corners with degrees 1, 2, 2, 3, 3, 5(i) How many edges does G have?(ii)If G were planar, how many facets would it have(iii) Determine whether G has an Euler path
QUESTION 2 Part 1: Use the graph shown to the right and the nearest- neighbor algorithm to find a Hamilton circuit that begins at vertex C 14 Be PD The weight of the circuit is 10 Part 2: 4 11 Use the best edge algorithm to find a Hamilton circuit. List the circuit beginning at vertex E. 7.
1. Use Dijkstra's algorithm to find the shortest path length between the vertices a and z in each of the following weighted graphs. (a) (b) a a 2 1 2 1 2 d 3 b d b f 2 4 4 5 3 1 с e 7 g с e 1 6 2
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Introduction To Discrete Mathematics: 1. Use Euclid’s Algorithm to calculate gcd(235, 145).2. Find a solution to 235x + 145y = 5.
9. For the question use Fluery's Algorithm. Go to the slide 18 -21 in the PowerPoint of the Sec 14.2 and follow similar steps with at least 4 figures to find your Euler Circuit. Start the Euler Circuit at B. E C. A
Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination. (a) For the forward recursion formulation of this problem, how many stages are there, and what arethe states for each stage? Stage 1: n = 1 Stage 2: n = 2 origin) ( Stage 3: n = 3 S A B C (b) Use forward recursion to solve this problem. However, instead of using the usual tables, show your work graphically. In particular, start with the given network, where the answers already are given for f (Sn) for four of the nodes; then solve for and fill in f2 (B) and fi* (0). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T. (c) Use forward recursion to solve this problem by manually constructing the usual tables for n = 3, n = 2, and n = 1.…

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