Consider a complete graph with 6 vertices labeled A, B, ... F. (a) If you can start at any vertex, how many Hamiltonian circuits exist? (b) If you can start at any vertex, how many different Hamiltonian circuits exist if a circuit and its mirror image are not counted as separate circuits? (c) If you start at vertex B, how many different Hamiltonian circuits exist if a circuit and its mirror image are not counted as separate circuits?

Consider a complete graph with 6 vertices labeled A, B, ... F. (a) If you can start at any vertex, how many Hamiltonian circuits exist? (b) If you can start at any vertex, how many different Hamiltonian circuits exist if a circuit and its mirror image are not counted as separate circuits? (c) If you start at vertex B, how many different Hamiltonian circuits exist if a circuit and its mirror image are not counted as separate circuits?

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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Question

Consider a complete graph with 6 vertices labeled A, B, ... F.
(a) If you can start at any vertex, how many Hamiltonian circuits exist?
(b) If you can start at any vertex, how many different Hamiltonian circuits exist if a circuit and its mirror image are not
counted as separate circuits?
(c) If you start at vertex B, how many different Hamiltonian circuits exist if a circuit and its mirror image are not counted
as separate circuits?

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