Problem A5: For each graph G and H below, determine whether it has a hamiltonian cycle. Justify your answer, by showing the hamiltonian cycle if it exists, or proving that it does not exist. (11) (12) (13) (14) (21) (31) (41) (22) (42) 23 (33) (43) (24) 34 (44) G (22) (32) (13) (23 (33) (14) (24) (34) (25) H
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- question 5. Draw an Eulerian graph and a Hamiltonian graph, both of more than four vertices.Given the preconditions for x and y as |x – y| ≤ 200, |2x + y - 150| ≤ 250, show the post-conditions for z = 3x2 + y2 + 3xy – 7x – 8y + 10. Please solve this problem mathematically and draw a 2D graph to show the covered domain for x and y. Please use MATLABIn each part, either draw a graph with the given specifications or explain why no such graph exists. A graph with 4 vertices that has a Euler circuit but no Hamiltonian circuits.
- 1. Find the slope of the line joining given point (2/3,-1/2) (5/6,-1/2) 2. Reduce the following equation to the form indicated (a) 5x-6y-13=0 :slope-intercept form (b) 2x+7y-14=0 :intercept form 3. Give the solution,graph and segment joining (-4, 7) and ( 5, -2) is divided into two segment one of which is five times as long as the other find the point division. 4. give the solution, graph and if the point (3, y) is equidistant from ( 5, -2 ) and (-1,4) find y 5. Give the solution, graph and per letter write the equation of the line through the given point of (a) parallel (b) perpendicular to the given line Point:(3,5) Line: y-axisDefine Hamiltonian path, Hamiltonian circuit and Hamiltonian graph and give one example each with justification. Write atleast two properties of Hamiltonian graph.What theorem helps identify or determine the existence of a Hamiltonian circuit on a connected graph? a. Hamiltonian Theorem b. Daren’s Theorem c. Eulerian Graph Theorem d. Dirac’s Theorem
- Construct a Halmilton Cycle within the provided graph. The cycle must start from H point.(b) Which of the circuits found in part (a) gives the best solution to the problem of finding a minimum Hamilton circuit for the graph? Select all that apply.Consider the function as given. (a) Use a computer algebra system to graph the function and use the graph to approximate the critical numbers visually. (b) Use a computer algebra system to find f′ and approximate the critical numbers. Are the results the same as the visual approximation in part (a)? Explain.
- Problem 3: Find the points on a circle of its octants with the circle centered at(5,5)and has a radius of 8 units. (with the aid of the table shows the result) Problem 4: Translate the triangleABChas vertices[A(−8,6),B(−8,9),C(−4,6)]+9units in thex-direction and−4in they-direction. (with the aid of the graph, show the result) Problem 5: Determine the coordinate of the vertices of triangleABC[A(−8,7),B(−3,7),C(−4,3)]after a counterclockwise rotation of180∘around the origin. (with the aid of the graph, show the result)Given the preconditions for x and y as |x – y| ≤ 200, |2x + y - 150| ≤ 250, show the post-conditions for z = 3x2 + y2 + 3xy – 7x – 8y + 10. Please solve this problem mathematically and draw a 2D graph to show the covered domain for x and y. plot in octavefor the 8 Quean problem answer the following 1- Given an example of a chromosome that represent a state of the solution and explain its content 2- Give two chromosomes and show their value after cross-over