Videos
For the graph shown in Fig. 6-19,
a. find three different Hamilton circuits.
b. find a Hamilton path that starts at A and ends at B.
c. find a Hamilton path that starts at D and ends at F.
(a)
To find:
Three Hamilton circuits for given graph.
Answer to Problem 1E
Solution:
The Hamilton circuit are
Explanation of Solution
Given:
The given figure is,
Approach:
A Hamilton circuit is the circuit that starts and ends at the same vertex and includes every other vertex of the graph only once.
Calculation:
Let’s start with vertex A the options to go forward are vertices B, D, F, and G, go to vertex B. From vertex B the options to move further are C, D, E, and G, go to vertex D. From vertex D the option to go forward is vertex C. From vertex C the option to move forward to is E. From vertex E the option to move forward to is F. From vertex F the option to move forward to is G. From vertex G the option to move forward to is A.
The Hamilton circuit is
Let’s start with vertex A the options to go forward are vertices B, D, F, and G, go forward with vertex G. From vertex G the options to move further are B and F, go forward with vertex B. From vertex B the options to go forward are vertices C, D, and E, go to vertex D. From vertex D the option to move forward to is C. From vertex C the option to move forward to is E. From vertex E the option to move forward to is F. From vertex F the option to move forward to is A.
The Hamilton circuit is
Let’s start with vertex A the options to go forward are vertices B, D, F, and G, go forward with vertex D. From vertex D the options to move further are B and C, go forward with vertex B. From vertex B the options to go forward are vertex C and E, go to vertex E. From vertex E the option to move forward to is C. From vertex C the option to move forward to is F. From vertex F the option to move forward to is G. From vertex G the option to move forward to is A.
The Hamilton circuit is
Conclusion:
Thus, the Hamilton circuits are
(b)
To find:
A Hamilton path that starts at A and ends at B.
Answer to Problem 1E
Solution:
A Hamilton path that starts at A and ends at B is
Explanation of Solution
Given:
The given figure is,
Approach:
A Hamilton path is the path that includes every other vertex of the graph only once.
Calculation:
Let’s start with vertex A the options to go forward are vertices B, D, F, and G, go forward with vertex G. From vertex G the options to move further are B and F, go forward with vertex F. From vertex F the options to go forward are vertex C, E, and G, go to vertex E. From vertex E the option to move forward to are B and C, go to vertex C. From vertex C the option to move forward to are B and D, go to vertex D. From vertex D the option to move forward to is B.
The Hamilton path is
Conclusion:
Thus, a Hamilton path that starts at A and ends at B is
(c)
To find:
A Hamilton path that starts at D and ends at F.
Answer to Problem 1E
Solution:
A Hamilton path that starts at D and ends at F is
Explanation of Solution
Given:
The given figure is,
Approach:
A Hamilton path is the path that includes every other vertex of the graph only once.
Calculation:
Let’s start with vertex D the options to go forward are vertices A, B, C, go forward with vertex C. From vertex C the options to move further are B, E and F, go forward with vertex E. From vertex E the options to go forward are vertex B and F, go to vertex B. From vertex B the option to move forward to are A and G, go to vertex G. From vertex G the option to move forward to are A and F, go to vertex A. From vertex A the option to move forward to is F.
The Hamilton path is
Conclusion:
Thus, a Hamilton path that starts at D and ends at F is
Want to see more full solutions like this?
Chapter 6 Solutions
MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
Additional Math Textbook Solutions
A First Course in Probability (10th Edition)
University Calculus
Elementary Statistics: A Step By Step Approach
Algebra and Trigonometry (6th Edition)
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
- Let H = span {u, v}. For each of the following sets of vectors determine whether H is a line or a plane. Select an Answer u = 3 1. -10 8-8 -2 ,v= 5 Select an Answer -2 u = 3 4 2. + 9 ,v= 6arrow_forwardRefer to page 20 for orthogonalizing a set of vectors using the Gram-Schmidt process. Instructions: • Apply the Gram-Schmidt procedure to the given set of vectors, showing all projections and subtractions step-by-step. • Normalize the resulting orthogonal vectors if required. • Verify orthogonality by computing dot products between the vectors. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 54 for solving the wave equation. Instructions: • Apply d'Alembert's solution method or separation of variables as appropriate. • Clearly show the derivation of the general solution. • Incorporate initial and boundary conditions to obtain a specific solution. Justify all transformations and integrations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]arrow_forward
- Refer to page 14 for calculating eigenvalues and eigenvectors of a matrix. Instructions: • Compute the characteristic polynomial by finding the determinant of A - XI. • Solve for eigenvalues and substitute them into (A - I) x = 0 to find the eigenvectors. • Normalize the eigenvectors if required and verify your results. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardExilet x = {a,b.c}dex.x―R> d(a,b) = d(b, c)=1' d(a, c) = 2 d(xx)=0VXEX is (x.d) m.s or not? 3.4 let x= d ((x,y), (3arrow_forwardHiw Show that sup (0,1) = 1 الفصل الثاني * Dif: let {an} be Seq. then fan?arrow_forward
- There are four white, fourteen blue and five green marbles in a bag. A marble is selected from the bag without looking. Find the odds of the following: The odds against selecting a green marble. The odds in favour of not selecting a green marble The odds in favor of the marble selected being either a white or a blue marble. What is true about the above odds? Explainarrow_forwardQ2/ Determine the size of square footing to carry net allowable load of 400 kN. FS-3. Use Terzaghi equation assuming general shear failure. 400KN 1 m += 35" C=0.0 Ya = 18.15 kN/m³ +=25" C=50 kN/m² Ya 20 kN/m³arrow_forward4 x+3 and g(x)=x2-9 4X-10 2X --13) The domain of rational expression A) 1R. {-2,-8} AB -14) Let f(x) = B) 1R. {2,-4,-8} 4X-12 x² +6x-16 X3+7X²+12X ? C) 1R \ {-4,-3,0} then f(x) + g(x) is equal ro D) IR 2 A) B) c) D) x²-9 x2-9 x²-9 x+4 DB 5x-4 A B If + then the value of B is equal to X+1 A) 4 B) 2 C) 5 D) 3 4X 4x+4 С.В.... x2+5X+6 x2 (x-2)(x+1) X-2 AC 16 The solution set of the equation A){4} B) {-3} C){ 1} 17 The solution set of the equation A) (-3,-2) B) [-3,0) C)[-3,-2] D). [-2,0) BA -18) Which one of the following is proper fraction? 2x+4 ≤0 入×1 x+2x+4 (x+1)(x+2) 2x+4x+2 = 4 X+1 is equal to D). {-5} ≤0 A) x6 +4 2x+12 2X x +4 B) c) x2-9 AL 2x+12 D) x+4 14) let g(x) = [x-3],then g(-2) is equal to A) -5 B)-6 C)-3 D) 3 Part III work out (show every step cleary) (2pt) 20. E9) Find the solution set of the equation 2x+4 x+1 ≤0 P(x) (a) P(x) =≤0 2x+4 50 x+1 x+1≤ 2x+4 (x-1)(x-2) x= 1 or x=2 solution is {1.2} x-1=0 of x-2=0 x = 1 or = 2arrow_forward
- Please show as much work as possible to clearly show the steps you used to find each solution. If you plan to use a calculator, please be sure to clearly indicate your strategy. 1. The probability of a soccer game in a particular league going into overtime is 0.125. Find the following: a. The odds in favour of a game going into overtime. b. The odds in favour of a game not going into overtime. c. If the teams in the league play 100 games in a season, about how many games would you expect to go into overtime?arrow_forwardPlease show as much work as possible to clearly show the steps you used to find each solution. If you plan to use a calculator, please be sure to clearly indicate your strategy. 1. The probability of a soccer game in a particular league going into overtime is 0.125. Find the following: a. The odds in favour of a game going into overtime. b. The odds in favour of a game not going into overtime. c. If the teams in the league play 100 games in a season, about how many games would you expect to go into overtime?arrow_forwardPlease show as much work as possible to clearly show the steps you used to find each solution. If you plan to use a calculator, please be sure to clearly indicate your strategy. 1. The probability of a soccer game in a particular league going into overtime is 0.125. Find the following: a. The odds in favour of a game going into overtime. b. The odds in favour of a game not going into overtime. c. If the teams in the league play 100 games in a season, about how many games would you expect to go into overtime?arrow_forward
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell