Euler and Hamilton Circuits In Exercises 3 and 4, determine whether each sequence of vertices is a circuit, whether it is an Euler circuit, and whether it is a Hamilton circuit. Justify your answers.
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- Find All vertices that are adjacent to v1. O v4 O v2, v1, v3 V5 O e1,e2, e7 O v5, v2 O e6 v1, v2, v3, v5 e 1 VI es e2 e5 • V4 e7 e 3. V2 e6 V3arrow_forwardHamilton Paths and Hamilton Circuits Question #1: Determine whether the given path is a Hamilton path, a Hamilton circuit, or neither. Explain your answer. 15 6 Path: A-B-F-I-K-E-G-L-J-H-D-C K J Harrow_forwardWhich are circuits in the graph? If not, why not? (a) F→ E D C B A (b) D→BA→F→E→D (c) F→C B⇒ A (d) G→ F→B →A → F F (e) D→F→D⇒B⇒F→D ... OA. Yes, it is a circuit. OB. No, it is not a circuit. The edge joining vertices (Use a comma to separate answers as needed.) D is used more than once. OC. No, it is not a circuit. There is no edge joining vertices (Use a comma to separate answers as needed.) OD. No, it is not a circuit. It does not begin and end at the same vertex. F (a) Is F→E D→C→B-Aa circuit? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. E Garrow_forward
- Give an appropriate answer. Using the following graph, find an Euler circuit that begins and ends with vertex C. A F O B D C-D→A→ E→ F→ A→B →C→D C- D→A→E→ F→A→ B No Euler circuit exists. OC-D→A→ E→ F→A-→ B → Carrow_forwardWhat is the Hamiltonian circuit in the given graph below? B E F D А. E -B -C-D- A-F-E В. A-D-E-F - B-C-A C. B -F-C-E- D-A-B D. F-C-B-E- A-D-Farrow_forwardDiscrete Math Determine whether the directed graph shown has an Euler circuit or Euler path. Construct the Euler circuit or Euler path if one exists.arrow_forward
- Construct a closure table for the switching network. P Q [~P (NQ v P)] 1 1 ? v ? v ? v ? v 1 0 ? v ? v ? v ? v 0 1 ? v ? v ? v ? v ? v 0 0 ? v ? v ? v ? v ? v Use the closure table to determine the required conditions for the network to be closed. The network is closed if P and Q are both open. The network is closed if P is open and Q is closed. The network is closed if P is closed and Q is open. The network is always closed. O The network is never closed. Submit Answerarrow_forwardGive an appropriate answer. Using the following graph, find an Euler circuit that begins and ends with vertex C. F OB OC-D→A-→ E → F→ A→ B OC-D→A→ E → F→ A→ B → C → D OC-D-A → E →F→A-→ B → C O No Euler circuit exists.arrow_forwardDiscrete Math: Give an example of a topological sort, a maximal chain, and a maximal anti-chain in this grapharrow_forward
- Consider the tree diagram. Path number 1 B1 C2 2 1 1 3 B2 3 C2 1 5 4 3. B3 C2 C3 7 Find P(C,|B2) · P(B2). (Enter your answer as a fraction.) 151/4arrow_forwardEssentials of DISCRETE MATHEMATICS Section 2.6 - Graph Theory Q: For what values of n does Kn have an Euler circuit? Explain.arrow_forwardUse the Edge-Picking Algorithm to find a Hamiltonian circuit in the weighted graph. F E A-F-D-E-B-C-A A-D-B-F-E-C-A A-B-E-D-F-C-A O A-C-D-E-F-B-A O A-E-B-C-F-D-A D 2 B 3 сarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage