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arXiv · 1809.06084

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

Lu Lu·Qiongxiang Huang·Jiangxia Hou
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Abstract

It is known that the automorphism group of the elementary abelian $2$-group $Z_2^n$ is isomorphic to the general linear group $GL(n,F_2)$ of degree $n$ over $F_2$. Let $W$ be the collection of permutation matrices of order $n$. It is clear that $W\le GL(n,F_2)$. In virtue of this, we consider the Cayley graph $Cay(Z_2^n,S)$, where $S$ is the union of some orbits under the action of $W$. We call such graphs the orbit Cayley graphs over $Z_2^n$. In this paper, we give eight infinite families of strongly regular graphs among orbit Cayley graphs over $Z_2^n$, in which six families are new as we know. By the way, we formulate the spectra of orbit Cayley graphs as well.

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Lu Lu, Qiongxiang Huang, Jiangxia Hou. 2018-09-17. Infinite classes of strongly regular graphs derived from $GL(n,F_2)$. https://arxiv.org/abs/1809.06084

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