On generalized Moore geometries. I, II
type: Item
instance of: scholarly article
title: On generalized Moore geometries. I, II
zbMATH Open document ID: 0626.51006
DOI: 10.1016/0012-365X(87)90176-2
author: Frederick J. Fuglister
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The author finds a bound for the diameter d of a nontrivial generalized Moore geometry. Using formulas from \textit{E. Bannai} and \textit{T. Ito} [``Algebraic Combinatorics. I: Association schemes.'' (1984; Zbl 0555.05019)], in the first part he proves that the minimal polynomial must factor into factors of degree at most 3 over integers. Then he applies the rationalization method of \textit{R. M. Damerell} and \textit{M. A. Georgiacodis} [J. Lond. Math. Soc., II. Ser. 23, 1-9 (1981; Zbl 0467.05019)] followed by reduction \(modulo 2\) and \(modulo 3.\) He obtains a list of exponential diophantine equations, each of which turns out to have a finite number of solutions. The largest of these solutions is \(d=161.\) In the second part the diameter d of a generalized Moore geometry is shown to be at most 13. He applies various ad hoc methods on a case - by - case method to lower the bound. The author means that the bound 13 could be further reduced, although it seems difficult.
Mathematics Subject Classification ID: 51C05
Mathematics Subject Classification ID: 51E99
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 4017746
zbMATH Keywords: diameter
zbMATH Keywords: generalized Moore geometry
MaRDI profile type: Publication
cites work: On the Maximum Diameter of a Class of Distance-Regular Graphs
cites work: On Moore Geometries, I
cites work: On Moore geometries. II
cites work: The nonexistence of certain generalized polygons
cites work: On finite Moore geometries
cites work: The nonexistence of Moore geometries of diameter 4
cites work: On the existence of certain distance-regular graphs
cites work: On the existence of certain generalized Moore geometries. I
cites work: On the existence of certain generalized Moore geometries. II
cites work: The degree of the eigenvalues of generalized Moore geometries
full work available at URL: 0012-365x(87)90176-2
OpenAlex ID: W4206824158
description: scientific article; zbMATH DE number 4017746