G3 (a) Which of the previous graphs have a Hamiltonian path? (b) Which of the previous graphs have a Hamiltonian cycle? (c) Which of the previous graphs have an Eulerian trail? (d) Which of the previous graphs have an Eulerian circuit? GA
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- 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?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?The complete graph of K12 is: Only Euler Only Hamiltonian Both Neither
- FOR 1-3: Consider the following graphs: 1. Which of the graph/s above contains an Euler Trail? A. A and D B. B and C C. A, B, and C D. B, C, and D 2. Which of the graph/s above is/are Eulerian? A. None of the graphs B. Only B C. Only C D. B and C 3. Which of the graph/s above is/are Hamiltonian? A. A and B B. A and C C. A, B, and D D. A, C, and D FOR: 4-8: Consider the following graph: 4. What is the minimum distance between points C and F? A. 9 B. 10 C. 11 D. 12 5. Which of the following is a Hamiltonian Circuit for the given graph? A. AIBGCDEFHA B. DICBAIHGFED C. FIBAHGCDEF D. GFEIDCBAHG 6. What is the length of the Hamiltonian Circuit described in number 46? A. 35 B. 37 C. 39 D. 41 7. Which vertex in the given graph has the highest degree? A. Vertex C B. Vertex F C. Vertex H D. Vertex I 8. Which is referred to as an edge connecting the same vertex? A. Circuit B. Loop C. Path D. Repeated Edge 9. Which of the following statements is/are true? i. The vertices of K4 all have…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…Does a k6 graph have a Hamiltonian cycle?
- Which of the following is false? A.) Hamiltonian cycle can be converted to a Hamiltonian path by removing one of its edge. B.) Every graph that contains a Hamiltonian cycle also contains a Hamiltonian path and vice versa is true. C.) There may exist more than one Hamiltonian paths and Hamiltonian cycle in a graph. D.) A connected graph has as Euler trail if and only if it has at most two vertices of odd degreeThe graph with two vertices is Hamiltonian. True FalseWhich of the graphs has a Hamiltonian circuit? a. graphs 1 and 2 onlyb. graph 2 onlyc. graph 1 onlyd. graphs 2 and 3 onlye. graph 3 onlyf. graphs 1, 2, and 3
- Theorem 3.5 states the following: Let G be a loopless graph with at least three vertices, and no isolated vertices. Then G is 2-connected if and only if, for every pair {e, f} of edges of G, there is a cycle of G that contains both e and f.Welcome to Murphman’s Amusement Park! A guest of the park would like to start at the Entrance, walk along each of the midway streets (colored in grey) exactly once, and then leave at the Exit. Note that the railroad tracks are colored purple and are not midway streets. a.Draw a graph in the box above corresponding to this guest’s situation, and determine whether or not the graph has an Eulerian circuit, and if so, give one. If it does not, then explain why not. If the graph does not have an Eulerian circuit, determine whether it has an Eulerian path, and if it does, give one. If it does not, then explain why not. b. Is it possible for the guest to start at the Entrance, walk along all of the midway streets (colored in grey) exactly once, and then leave at the Exit?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.