Hokkaido Mathematical Journal

On strongly regular graphs with parameters (k,0,2) and their antipodal double covers

Nobuo NAKAGAWA

Full-text: Open access

Abstract

Let $\Gamma$ be a strongly regular graph with parameters $(k, \lambda, \mu)=(q^{2}+1,0,2)$ admitting $G(\cong PGL(2, q)2)$ as one point stabilizer for odd prime power $q$. We show that if $G$ stabilizes a vertex $x$ of $\Gamma$ and acts on $\Gamma_{2}(x)$ transitively, then $q=3$ holds and $\Gamma$ is the Gewirtz graph. Moreover it is shown that an antipodal double cover whose diameter 4 of a strongly regular graph with parameters $(k, 0, 2)$ is reconstructed from a symmetric association scheme of class 6 with parameters $p_{j.k}^{i}(0\leq i, j, k\leq 6)$ in the Section 3.

Article information

Source
Hokkaido Math. J., Volume 30, Number 2 (2001), 431-450.

Dates
First available in Project Euclid: 22 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1350911961

Digital Object Identifier
doi:10.14492/hokmj/1350911961

Mathematical Reviews number (MathSciNet)
MR1844827

Zentralblatt MATH identifier
0982.05114

Subjects
Primary: 05E30: Association schemes, strongly regular graphs
Secondary: 20B20: Multiply transitive finite groups

Keywords
antipodal cover of strongly regular graph association scheme finite transitive group

Citation

NAKAGAWA, Nobuo. On strongly regular graphs with parameters (k,0,2) and their antipodal double covers. Hokkaido Math. J. 30 (2001), no. 2, 431--450. doi:10.14492/hokmj/1350911961. https://projecteuclid.org/euclid.hokmj/1350911961


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