自由数独图的谱
Spectrum of free-form Sudoku graphs
摘要：
一个自由形式的数独问题是一个正方形排列的m乘以m的细胞，使细胞被分割成m个子集（称为块）的相等基数。这个谜题的目标是把整数1，.，m，这样每行、每列和每块中的数字都是不同的。用一个顶点表示每个单元格，并在两个顶点之间添加边，根据规则，相应的单元格必须包含不同的数字。这产生了相关的自由形式数独图。本文研究了自由数独图的特征值，特别是完整性。此外，我们分析了演化的特征值和特征空间的这种图形时，相关的难题是受到一个“吹”操作，缩放单元格，包括其块分区。
英文摘要：
A free-form Sudoku puzzle is a square arrangement of m times m cells such that the cells are partitioned into m subsets (called blocks) of equal cardinality. The goal of the puzzle is to place integers 1,...,m in 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, scaling the cell grid including its block partition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
