## Hokkaido Mathematical Journal

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

Nobuo NAKAGAWA

#### 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

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

#### 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