Let G be the following graph. V1 V3 V5 VA (a) Let A be the adjacency matrix of G. Find A. (b) Using only A and its powers, determine how many walks of length EXACTLY 3 are there starting at 2 and ending at 4. Explain. (c) Using only A and its powers, determine how many walks of length AT MOST 3 are there starting at 2 and ending at v4. Explain.

Let G be the following graph. V1 V3 V5 VA (a) Let A be the adjacency matrix of G. Find A. (b) Using only A and its powers, determine how many walks of length EXACTLY 3 are there starting at 2 and ending at 4. Explain. (c) Using only A and its powers, determine how many walks of length AT MOST 3 are there starting at 2 and ending at v4. Explain.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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9. Let G2 be depicted in the following diagram: b h a d 9(d) Give an example of a walk of length five in G2 that is not a path.
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Which are walks in the graph? If not, why not? (a) F→ DC (b) ABG (c) DE F→C (d) DB→ F→D⇒B (e) C → B (f) G-F→G F -----/ B A D OA. Yes, it is a walk. OB. No, it is not a walk. It does not begin and end at the same vertex. OC. No, it is not a walk. The edge joining vertices is used more than once. (Use a comma to separate answers as needed.) OC. No, it is not a walk. There is no edge joining vertices (Use a comma to separate answers as needed.) OD. No, it is not a walk. It does not begin and end at the same vertex. F OA. Yes, it is a walk. OB. No, it is not a walk. The edge joining vertices is used more than once. (Use a comma to separate answers as needed.) E (e) Is C → B a walk? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. G ... OD. No, it is not a walk. There is no edge joining vertices (Use a comma to separate answers as needed.) (f) Is G→F→G → F a walk? Select the correct choice below and, if necessary, fill in the answer box to…