56 research outputs found
A general construction of strictly Neumaier graphs and related switching
In this paper we propose a construction of Neumaier graphs with nexus 1,
which generalises two known constructions. We then discuss small strictly
Neumaier graphs obtained from the general construction and give a geometric
description for some of them. Finally, we apply a variation of the Godsil-McKay
switching to the general construction
New strongly regular graphs from finite geometries via switching
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. (C) 2019 Elsevier Inc. All rights reserved
New Strongly Regular Graphs from Finite Geometries via Switching
We show that the strongly regular graph on non-isotropic points of one type
of the polar spaces of type , , , , and
are not determined by its parameters for . 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.Comment: 13 pages, accepted in Linear Algebra and Its Application
Graphs Cospectral with Kneser Graphs
AMS Subject Classification: 05C50Kneser graph;Johnson scheme;Spectral characterization
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