\input zb-basic
\input zb-ioport
\iteman{io-port 05808532}
\itemau{Klotz, Walter; Sander, Torsten}
\itemti{How does Sudoku acquire integral eigenvalues? (Wie kommt Sudoku zu ganzzahligen Eigenwerten?)}
\itemso{Math. Semesterber. 57, No. 2, 169-183 (2010).}
\itemab
Summary: Sudoku provides points of contact to different areas of mathemtatics. We hit on connections with combinatorics, graph theory, group theory and with linear algebra. Each Sudoku puzzle turns out to be a graph theoretical colouring problem. The underlying Sudoku graph is a highly symmetric Cayley graph. A special feature of this graph is that it (also for larger formats $n^2 \times n^2$, $n \ge 3$, of the puzzle) possesses exactly six different integral eigenvalues. For all formats $n^2 \times n^2$ of the puzzle we determine all eigenvalues of the corresponding Sudoku graph.
\itemrv{~}
\itemcc{}
\itemut{Sudoku puzzle; Sudoku graph; Cayley graph; integral eigenvalue}
\itemli{doi:10.1007/s00591-010-0076-4}
\end