On strongly regular graph with parameters (65; 32; 15; 16)

2021/02/10 by O. V. Gritsenko, Gritsenko, Oleg · 3 citations
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2102.05432

openalex publication_date 2021/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a strongly regular graph with the parameters (65; 32; 15; 16). The idea is to search for an adjacency matrix that consists of circulant blocks. Equations with such matrices can be reduced to congruences with polynomials matrices of smaller orders. We can consider these congruences over different moduli for a more efficient computational approach.

Cited by

• Thin divisible designs graphs: an interplay between fixed-point free involutions of (v,k,λ)-graphs and symmetric weighing matrices
• On the existence of directed strongly regular graphs with parameters (22, 9, 6, 3, 4)
• Finite permutation groups with quasi-semiregular elements

Related

• On the existence of directed strongly regular graphs with parameters (22, 9, 6, 3, 4)
• Construction of Directed Strongly Regular Graphs Using Block Matrices
• There does not exist a strongly regular graph with parameters (1911,270,105,27)
• Complex Hadamard Matrices and Strongly Regular Graphs
• There is no strongly regular graph with parameters (460,153,32,60)