Try Magic Notes and save time.Try it free
Try Magic Notes and save timeCrush your year with the magic of personalized studying.Try it free
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

Verified
Step 1
1 of 3

The 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.

## Recommended textbook solutions

#### A First Course in Abstract Algebra

7th EditionISBN: 9780201763904John B. Fraleigh
2,398 solutions

#### Abstract Algebra

3rd EditionISBN: 9780471433347David S. Dummit, Richard M. Foote
1,960 solutions

#### Contemporary Abstract Algebra

8th EditionISBN: 9781133599708Joseph Gallian
1,976 solutions

#### Contemporary Abstract Algebra

9th EditionISBN: 9781305657960Joseph Gallian
1,687 solutions