Uniqueness of strongly regular graphs having minimal \(p\)-rank
Let \(\Gamma\) be a strongly regular graph with adjacency matrix \(A\). Let \(I\) be the identity matrix and let \(p\) be a prime. We study the \(p\)-ranks of the matrices \(A + cI\) for integral \(c\) and want to characterize among all strongly regular graphs with a given parameter set those for which a \(p\)-rank is minimal. After mentioning which \(p\)-ranks of a strongly regular graph are not determined by these parameters we use these relevant \(p\)-ranks as extra parameters to characterize strongly regular graphs. Four classes of strongly regular graphs are discussed: Paley graphs, latin square graphs, symplectic graphs and collinearity graphs of generalized quadrangles with four points per line.
scientific article; zbMATH DE number 803726
scientific article