Your friend Sue has a graph with eight vertices, labeled Vertex A, Vertex B, Vertex C,...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Your friend Sue has a graph with eight vertices, labeled Vertex A, Vertex B, Vertex C, Vertex D, Vertex E, Vertex X, Vertex Y, and Vertex Z. The graph has nine edges, which are: АВ, АЕ, ВС, СD, CX, CZ, DE, XY, Y Z. Sue has arranged these nine edges into two mini-cycles: Mini-cycle 1: AB, BC, CD, DE, EA; Mini-cycle 2: XY, Y Z, ZC, CX. Can you help Sue put together her mini-cycles to get a full Euler cycle for the graph? Make sure to record the Euler cycle, and explain how you arrived at it. • Part B (3 pts): Cycle City consists of four islands, labeled A, B, C, and D. There are various bridges to help the residents get from island to island. The map is pictured below. The circles represent the islands, and the lines between circles (some curved, some straight) represent the bridges between islands. A B D The mayor of Cycle City, Bob the Bicyclist, would like to find a way to start at Island A, then bike around the island, using every bridge exactly once, so that he ends up back on Island A. Unfortunately, this is not possible. Explain why (you can freely use any theorems stated in class). • Part C (3pts): Bob the Bicyclist would like to add some bridges to Cycle City (pictured in Part B) so that he can start at Island A, bike around, using every bridge exactly once, and end up at A again. How many new bridges must he build? For full credit, explain why your answer is optimal (i.e., why you couldn't get away with fewer new bridges). Your friend Sue has a graph with eight vertices, labeled Vertex A, Vertex B, Vertex C, Vertex D, Vertex E, Vertex X, Vertex Y, and Vertex Z. The graph has nine edges, which are: АВ, АЕ, ВС, СD, CX, CZ, DE, XY, Y Z. Sue has arranged these nine edges into two mini-cycles: Mini-cycle 1: AB, BC, CD, DE, EA; Mini-cycle 2: XY, Y Z, ZC, CX. Can you help Sue put together her mini-cycles to get a full Euler cycle for the graph? Make sure to record the Euler cycle, and explain how you arrived at it. • Part B (3 pts): Cycle City consists of four islands, labeled A, B, C, and D. There are various bridges to help the residents get from island to island. The map is pictured below. The circles represent the islands, and the lines between circles (some curved, some straight) represent the bridges between islands. A B D The mayor of Cycle City, Bob the Bicyclist, would like to find a way to start at Island A, then bike around the island, using every bridge exactly once, so that he ends up back on Island A. Unfortunately, this is not possible. Explain why (you can freely use any theorems stated in class). • Part C (3pts): Bob the Bicyclist would like to add some bridges to Cycle City (pictured in Part B) so that he can start at Island A, bike around, using every bridge exactly once, and end up at A again. How many new bridges must he build? For full credit, explain why your answer is optimal (i.e., why you couldn't get away with fewer new bridges).
Expert Answer:
Related Book For
Fundamentals of Physics
ISBN: 978-0471758013
8th Extended edition
Authors: Jearl Walker, Halliday Resnick
Posted Date:
Students also viewed these mathematics questions
-
Two identical slender rods AB and BC are welded together to form an L-shaped assembly. The assembly is pressed against a spring at D and released from the position shown. Knowing that the maximum...
-
Two identical 10-lb slender rods AB and BC are welded together to form an L-shaped assembly which is suspended from a hinge at B and is at rest in a vertical plane. A 0.03-lb bullet strikes the...
-
The figure shows two circles C and D of radius 1 that touch at P.T is a common tangent line; C1 is the circle that touches C, D, and T; C2 is the circle that touches C, D, and C1; C3 is the circle...
-
Fill in each blank so that the resulting statement is true. I find (f g)(x) by replacing each occurrence of x in the equation for_______ with________ .
-
For every positive integer n, show that O-O) () + ()} +. +. 2.
-
Prove Theorem 2.11: If g is continuous at a and f is continuous at g(a), then the composition f g is continuous at a. (Hint: Write the definition of continuity for f and g separately; then combine...
-
If the interest rate at B is 20 percent, then which of the following best describes the analysis of the investment? a. The IRR of the investment is less than 20 percent. b. The IRR of the investment...
-
The following facts relate to Duncan Corporation. 1. Deferred tax liability, January 1, 2008, $60,000. 2. Deferred tax asset, January 1, 2008, $20,000. 3. Taxable income for 2008, $105,000. 4....
-
1. Application of Legendre transform on van der Waal gas: For monatomic van der Waal gas, the entropy is 3/21 N2a\ S (E,V,N) = Ng In V-Nb 4m E + N 3h2 N 5 V 2 Where KB, m, , h, a, b are constants....
-
An engineer has performed an experiment to study the effect of four factors on the surface roughness of a machined part. The factors (and their levels) are A = tool angle (12, 15), B = cutting fluid...
-
What are the three big steps in achieving Personal Development?
-
Mike leases a new pickup by paying $3200 up front and $259 a month over three years. The lease also stipulates he will be charged $0.15 per mile for every mile over 36,000. If he puts 39,928 miles on...
-
Linda is analyzing two machines to determine which one it should purchase for syracuse Inc. Machine A has an initial cost of $462,000, annual after-tax cash outflows of $46,200, and a four-year life....
-
Simplify the following completely: 45x5 A) 5x3
-
Tommy Appleton is in charge of arranging the social hour period and dinner for the monthly meetings of the local chapter of the Management Accountants Association. Tommy is negotiating with a new...
-
During 2013, Parker Enterprises generated revenues of $60,000. The company's expenses were as follows: cost of goods sold of $30,000, operating expenses of $12,000 and a loss on the sale of equipment...
-
1. Select the theory posited by either Karl Marx or Emile Durkheim on how industrialization changed the nature of work and explain the theoretical perspective as proposed by your selected theorist....
-
Inexhaustible collections of ONPOs are not required to be capitalized or depreciated, if certain criteria are met. Why is this so, and what accounting and reporting recognition, if any, is required...
-
The uniform rod (length 0.60 m, mass 1.0 kg) in Figure rotates in the plane of the figure about an axis through one end, with a rotational inertia of 0.12 kg ? m2. As the rod swings through its...
-
Use the conservation laws and Tables 44-3 and 44-4 to identify particle x in each of the following reactions, which proceed by means of the strong interaction: (a) p + p p + A 0 + x; (b) p + p n +...
-
The frequency of oscillation of a certain LC circuit is 200 kHz. At time t = 0, plate A of the capacitor has maximum positive charge. At what earliest time t > 0 will (a) Plate A again has maximum...
-
A study of 16,405 adult daughters of women who immigrated to California from other countries measured the economic status of the daughters by the median household income Y for the ZIP code they lived...
-
Explain why you either agree or disagree with this interpretation of the results from estimating a regression model: This study concludes that the data are statistically substantial because there are...
-
The study described in the preceding exercise also looked at 11,794 first-born daughters at the time they gave birth to their first child. A least squares regression was used to examine the...
Study smarter with the SolutionInn App