2020/12/17 by Gary R. W. Greaves, Greaves, Gary R. W., Jack H. Koolen +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2012.09391
openalex publication_date 2020/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the order of a maximal clique in an amply regular graph with a fixed smallest eigenvalue by considering a vertex that is adjacent to some (but not all) vertices of the maximal clique. As a consequence, we show that if a strongly regular graph contains a Delsarte clique, then the parameter μ is either small or large. Furthermore, we obtain a cubic polynomial that assures that a maximal clique in an amply regular graph is either small or large (under certain assumptions). Combining this cubic polynomial with the claw-bound, we rule out an infinite family of feasible parameters (v,k,λ,μ) for strongly regular graphs. Lastly, we provide tables of parameters (v,k,λ,μ) for nonexistent strongly regular graphs with smallest eigenvalue -4, -5, -6 or -7.