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

TL;DR

This paper presents a novel construction of a strongly regular graph with specific parameters using circulant block matrices and polynomial congruences, enhancing computational efficiency.

Contribution

It introduces a new method for constructing strongly regular graphs via circulant block matrices and polynomial congruences, improving computational approaches.

Findings

Successfully constructed the strongly regular graph with parameters (65; 32; 15; 16)

Reduced equations to polynomial congruences for efficiency

Demonstrated the effectiveness of circulant block matrices in graph construction

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.