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 Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 501–515 (Mi semr1074)

Discrete mathematics and mathematical cybernetics

Minimum supports of eigenfunctions in bilinear forms graphs

E. V. Sotnikova

Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia

Abstract: In this paper we study eigenfunctions corresponding to the minimum eigenvalue of bilinear forms graphs. Our main goal is to find eigenfunctions with the supports (non-zero positions) of minimum cardinality. For bilinear forms graphs of diameter $D=2$ over a prime field we prove that there exist eigenfunctions with the support achieving the weight distribution bound. We also provide an explicit construction of such functions. For bilinear forms graphs of diameter $D\ge 3$ we show the non-existance of eigenfunctions with supports achieving the weight distribution bound.

Keywords: bilinear forms graph, eigenfunctions, minimum supports, distance-regular graphs.

 Funding Agency Grant Number Russian Science Foundation 18-11-00136 This work was funded by the Russian Science Foundation under grant 18-11-00136.

DOI: https://doi.org/10.33048/semi.2019.16.032

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Bibliographic databases:

Document Type: Article
UDC: 519.177
MSC: 05C50
Received December 30, 2018, published April 12, 2019
Language: English

Citation: E. V. Sotnikova, “Minimum supports of eigenfunctions in bilinear forms graphs”, Sib. Èlektron. Mat. Izv., 16 (2019), 501–515

Citation in format AMSBIB
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