Finite analogues of non-Euclidean spaces and Ramanujan graphs.

DOI10.1016/S0195-6698(03)00110-0zbMath1033.05099MaRDI QIDQ1427974

Osamu Shimabukuro, Hajime Tanaka, Eiichi Bannai

Publication date: 14 March 2004

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (12)

Eigenvalues of Cayley graphs ⋮ The number of occurrences of a fixed spread among \(n\) directions in vector spaces over finite fields ⋮ The sovability of norm, bilinear and quadratic equations over finite fields via spectra of graphs ⋮ Symmetric association schemes attached to finite upper half planes over rings. ⋮ Sets with integral distances in finite fields ⋮ On 3rd and 4th moments of finite upper half plane graphs ⋮ Distinct distances between points and lines in \(\mathbb{F}_q^2\) ⋮ Distinct distances on regular varieties over finite fields ⋮ Extension theorems and a connection to the Erdős-Falconer distance problem over finite fields ⋮ Commutative association schemes ⋮ Finite Euclidean graphs and Ramanujan graphs ⋮ Appendix: On some Gelfand pairs and commutative association schemes.

Cites Work

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• Finite Euclidean graphs and Ramanujan graphs
• On distance-regular graphs with fixed valency. IV
• Character table of a controlling association scheme defined by the general orthogonal group \(O(3,q)\)
• Character tables of certain association schemes coming from finite unitary and symplectic groups
• Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
• A four-class subscheme of the association of scheme coming from the action of \(\text{PGL} (2,4^f)\)
• Character tables of the association schemes of finite orthogonal groups acting on the nonisotropic points
• Spherical functions for finite upper half planes with characteristic 2
• ENNOLA TYPE DUALITIES IN THE CHARACTER TABLES OF SOME ASSOCIATION SCHEMES
• Estimates for Soto-Andrade sums.
• On the Riemann Hypothesis in Function-Fields
• A note on exponential sums

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