TY - JOUR

T1 - New strongly regular graphs from finite geometries via switching

AU - Ihringer, Ferdinand

AU - Munemasa, Akihiro

N1 - Publisher Copyright:
© 2019

PY - 2019/11/1

Y1 - 2019/11/1

N2 - We show that the strongly regular graph on non-isotropic points of one type of the polar spaces of type U(n,2), O(n,3), O(n,5), O+(n,3), and O−(n,3) are not determined by its parameters for n≥6. We prove this by using a variation of Godsil-McKay switching recently described by Wang, Qiu, and Hu. This also results in a new, shorter proof of a previous result of the first author which showed that the collinearity graph of a polar space is not determined by its spectrum. The same switching gives a linear algebra explanation for the construction of a large number of non-isomorphic designs.

AB - We show that the strongly regular graph on non-isotropic points of one type of the polar spaces of type U(n,2), O(n,3), O(n,5), O+(n,3), and O−(n,3) are not determined by its parameters for n≥6. We prove this by using a variation of Godsil-McKay switching recently described by Wang, Qiu, and Hu. This also results in a new, shorter proof of a previous result of the first author which showed that the collinearity graph of a polar space is not determined by its spectrum. The same switching gives a linear algebra explanation for the construction of a large number of non-isomorphic designs.

KW - Polar space

KW - Spectrum

KW - Strongly regular graph

KW - Switching

UR - http://www.scopus.com/inward/record.url?scp=85069489791&partnerID=8YFLogxK

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U2 - 10.1016/j.laa.2019.07.014

DO - 10.1016/j.laa.2019.07.014

M3 - Article

AN - SCOPUS:85069489791

SN - 0024-3795

VL - 580

SP - 464

EP - 474

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -