Abstract
AbstractA free-form Sudoku puzzle is a square arrangement ofm×mcells such that the cells are partitioned intomsubsets (called blocks) of equal cardinality. The goal of the puzzle is to place integers 1, . . ,min the cells such that the numbers in every row, column and block are distinct. Represent each cell by a vertex and add edges between two vertices exactly when the corresponding cells, according to the rules, must contain different numbers. This yields the associated free-form Sudoku graph. This article studies the eigenvalues of free-form Sudoku graphs, most notably integrality. Further, we analyze the evolution of eigenvalues and eigenspaces of such graphs when the associated puzzle is subjected to a ‘blow up’ operation, which scales the cell grid including its block partition.
Highlights
IntroductionThe recreational game of Sudoku has been popular for several years now
Lemma 4 tells us that no positive eigenvalue of FSud↑k (n, T ) originates from XB. It seems that free-form Sudokus have not been researched at all
We have presented the blow up operation and shown how to obtain the eigenvalues of blown up free-form Sudokus from their originals
Summary
The recreational game of Sudoku has been popular for several years now. Its classic variant is played on a board with 9 × 9 cells, subdivided into a 3 × 3 grid of square blocks containing 3 × 3 cells each. Each cell may be empty or contain one of the numbers 1, . A number of cells of each puzzle have been pre-filled by the puzzle creator. The goal of the puzzle solver is to fill the remaining cells with the numbers 1, . 9 such that in the completed puzzle the number of each cell occurs only once per row, column and block. The goal of the puzzle solver is to fill the remaining cells with the numbers 1, . . . , 9 such that in the completed puzzle the number of each cell occurs only once per row, column and block.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
