Regular partitions of (weak) finite generalized polygons
The authors define a regular \(m\)-partition of a distance regular graph \(\Gamma\) as a partition of the vertex set of \(\Gamma\) into \(m\) classes \(\mathcal P_i\), \(i= 1,\ldots m\), having the property that for any \(x \in \mathcal P_i\) the number of points, \(d_{ij}\), in \(\mathcal P_j\) adjacent to \(x\) depends only on \(i\), i.e., is independent of \(x\). They show that the eigenvalues of the matrix \((d_{ij})\) are strongly linked to those of the adjacency matrix of \(\Gamma\). They exploit this relationship to gain structural information on various substructures of finite generalized polygons. They are able to give unifying, alternative, and more elegant proofs of several results in the literature.
scientific article; zbMATH DE number 5536719
scientific article