**Question:**In a complete graph with 720 distinct Hamilton circuits, there is a total ofA) 6 vertices. B) 9 vertices. C) 7 vertices. D) 5 vertices.**Explanation:**A Hamilton circuit in a complete graph involves visiting every vertex exactly once and returning to the starting point. The number of Hamilton circuits in a complete graph with $ n $ vertices is given by the formula:\[\frac{(n-1)!}{2}\]Here, we know there are 720 distinct Hamilton circuits. Thus, we set up the equation:\[\frac{(n-1)!}{2} = 720\]Solving this would give us the number of vertices. Note that as a complete graph grows in the number of vertices, the number of possible Hamilton circuits grows factorially.

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Answered: 17) In a complete graph with 720…

17) In a complete graph with 720 distinct Hamilton circuits, there is a total of B) 9 vertices. A) 6 vertices. C) 7 vertices. D) 5 vertices.

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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