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This article is cited in 2 scientific papers (total in 2 papers)
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.
Received December 30, 2018, published April 12, 2019
Citation:
E. V. Sotnikova, “Minimum supports of eigenfunctions in bilinear forms graphs”, Sib. Èlektron. Mat. Izv., 16 (2019), 501–515
Linking options:
https://www.mathnet.ru/eng/semr1074 https://www.mathnet.ru/eng/semr/v16/p501
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Abstract page: | 285 | Full-text PDF : | 160 | References: | 30 |
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