A solution of a problem of A. E. Brouwer

Mikhail Muzychuk; István Kovács

doi:10.1007/s10623-004-4858-3

A solution of a problem of A. E. Brouwer

Mikhail Muzychuk, István Kovács

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let q = p^e ≡ 1(mod 4) be a prime power, and let Π^(q) be the Paley graph over the finite field double-struck F sign_q. Denote by Γ^(q) the subgraph of Π^(q) induced on the set of non-zero squares of double-struck F sign_q. In this paper the full automorphism group of r^(q) is determined affirming the conjecture of Brouwer [Des. Codes Cryptograph. 21, 69-76 (2000)]. The proof combines spectral and Schur ring techniques.

Original language	English
Pages (from-to)	249-264
Number of pages	16
Journal	Designs, Codes, and Cryptography
Volume	34
Issue number	2-3
DOIs	https://doi.org/10.1007/s10623-004-4858-3
State	Published - 1 Feb 2005
Externally published	Yes

Keywords

Automorphism groups
Paley graphs
Schur rings

ASJC Scopus subject areas

Computer Science Applications
Applied Mathematics

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10.1007/s10623-004-4858-3

Cite this

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abstract = "Let q = pe ≡ 1(mod 4) be a prime power, and let Π(q) be the Paley graph over the finite field double-struck F signq. Denote by Γ(q) the subgraph of Π(q) induced on the set of non-zero squares of double-struck F signq. In this paper the full automorphism group of r(q) is determined affirming the conjecture of Brouwer [Des. Codes Cryptograph. 21, 69-76 (2000)]. The proof combines spectral and Schur ring techniques.",

keywords = "Automorphism groups, Paley graphs, Schur rings",

author = "Mikhail Muzychuk and Istv{\'a}n Kov{\'a}cs",

note = "Funding Information: The first author was partially supported by the Israeli Ministry of Absorption. The research of the second author was partially supported by OTKA Grant F-030737 and T-043758. This paper was started during a two-week visit of the second author at Ben-Gurion University of the Negev. This visit was partially supported by the Ben-Gurion University of the Negev and the Netanya Academic College.",

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N2 - Let q = pe ≡ 1(mod 4) be a prime power, and let Π(q) be the Paley graph over the finite field double-struck F signq. Denote by Γ(q) the subgraph of Π(q) induced on the set of non-zero squares of double-struck F signq. In this paper the full automorphism group of r(q) is determined affirming the conjecture of Brouwer [Des. Codes Cryptograph. 21, 69-76 (2000)]. The proof combines spectral and Schur ring techniques.

AB - Let q = pe ≡ 1(mod 4) be a prime power, and let Π(q) be the Paley graph over the finite field double-struck F signq. Denote by Γ(q) the subgraph of Π(q) induced on the set of non-zero squares of double-struck F signq. In this paper the full automorphism group of r(q) is determined affirming the conjecture of Brouwer [Des. Codes Cryptograph. 21, 69-76 (2000)]. The proof combines spectral and Schur ring techniques.

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A solution of a problem of A. E. Brouwer

Abstract

Keywords

ASJC Scopus subject areas

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