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Question

$\begin{array} { l } { \text { Find a Hamiltonian circuit in } } \\ { \text { Cay } \left( \{ ( a , 0 ) , ( b , 0 ) , ( e , 1 ) \} : Q _ { 4 } \oplus Z _ { m } \right) } \\ { \text { where } m \text { is even. } } \end{array}$

Solution

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1 of 3The following is a Hamiltonion circuit for the Cayley diagraph $Cay(\{(a,0),(b,0),(e,1)\}:Q_4\oplus \mathbb Z_4)$ obtained by chaining two copies of the solution to $\textbf{exercise 2}$ together. For $n$ an arbitrary even number we can repeat the same technique using $\frac{n}{2}$ copies.

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