English

Infinite classes of strongly regular graphs derived from $GL(n,F_2)$

Combinatorics 2018-09-18 v1

Abstract

It is known that the automorphism group of the elementary abelian 22-group Z2nZ_2^n is isomorphic to the general linear group GL(n,F2)GL(n,F_2) of degree nn over F2F_2. Let WW be the collection of permutation matrices of order nn. It is clear that WGL(n,F2)W\le GL(n,F_2). In virtue of this, we consider the Cayley graph Cay(Z2n,S)Cay(Z_2^n,S), where SS is the union of some orbits under the action of WW. We call such graphs the orbit Cayley graphs over Z2nZ_2^n. In this paper, we give eight infinite families of strongly regular graphs among orbit Cayley graphs over Z2nZ_2^n, in which six families are new as we know. By the way, we formulate the spectra of orbit Cayley graphs as well.

Keywords

Cite

@article{arxiv.1809.06084,
  title  = {Infinite classes of strongly regular graphs derived from $GL(n,F_2)$},
  author = {Lu Lu and Qiongxiang Huang and Jiangxia Hou},
  journal= {arXiv preprint arXiv:1809.06084},
  year   = {2018}
}