2011/06/05 by Norman Biggs, Biggs, Norman · 1 citation
Computer Science · Engineering · Mathematics · #05C50 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1106.0889
openalex publication_date 2011/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An approach to the enumeration of feasible parameters for strongly regular graphs is described, based on the pair of structural parameters (a,c) and the positive eigenvalue e. The Krein bound ensures that there are only finitely many possibilities for c, given a and e, and the standard divisibility conditions can be used to reduce the possibilities further. Many sets of feasible parameters appear to be accidents of arithmetic, but in some cases the conditions are satisfied for algebraic reasons. As an example, we discuss an infinite family of feasible parameters for which the corresponding graphs necessarily have a closed neighborhood as a star complement for e.