English

Switched graphs of some strongly regular graphs related to the symplectic graph

Combinatorics 2016-05-25 v1

Abstract

Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters (2n±2(n1)/2,2n1±2(n1)/2,2n2±2(n3)/2,2n2±2(n1)/2)(2^n\pm2^{(n-1)/2},2^{n-1}\pm2^{(n-1)/2},2^{n-2}\pm2^{(n-3)/2},2^{n-2}\pm2^{(n-1)/2}) are constructed for any odd n5n \geq 5. The construction is described in terms of geometry of quadric in projective space. The binary linear codes of the switched graphs are [2n2n12,n+3,2t+1]2[2^n \mp 2^{\frac{n-1}{2}},n+3,2^{t+1}]_2-code or [2n2n12,n+3,2t+2]2[2^n \mp 2^{\frac{n-1}{2}},n+3,2^{t+2}]_2-code.

Keywords

Cite

@article{arxiv.1605.07400,
  title  = {Switched graphs of some strongly regular graphs related to the symplectic graph},
  author = {Alice M. W. Hui and Bernardo Rodrigues},
  journal= {arXiv preprint arXiv:1605.07400},
  year   = {2016}
}