On amply regular locally \(GQ(4, 6)\)-graphs
type: Item
instance of: scholarly article
title: On amply regular locally \(GQ(4, 6)\)-graphs
zbMATH Open document ID: 1276.05019
DOI: 10.1134/S106456241203012X
author: Dmitriĭ Viktorovich Paduchikh
author: Madina Mukhadinovna Khamgokova
author: Alexandre A. Makhnev
published in: Doklady Mathematics
publication date: 2012-11-15T00:00:00Z
review text: An undirected \(k\)-regular graph with \(v\) vertices is called an amply regular graph with parameters \((v, k, \lambda, \mu)\) if any two adjacent vertices have exactly \(\lambda\) common neighbours and any two vertices of distance 2 apart have exactly \(\mu\) common neighbours. In an incidence structure \((P, {\mathcal B})\) (without multiple blocks) with point set \(P\) and block set \({\mathcal B}\), if any two blocks intersect in at most one point, then the blocks are called lines and the geometry \((P, {\mathcal B})\) is called a partial space. A partial space of order \((s, t)\) (that is, each line contains precisely \(s+1\) points and each point lies on precisely \(t+1\) lines) is called a generalised quadrangle, denoted \(GQ(s,t)\), if any antiflag \((a, L)\) there is a unique line containing \(a\) and intersecting \(L\).
reviewed by: Sanming Zhou
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 6106457
zbMATH Keywords: Amply regular graph
zbMATH Keywords: generalised quadrangle
zbMATH Keywords: locally \(GQ(s, t)\)-graph
MaRDI profile type: Publication
cites work: Locally GQ(3,5)-graphs and geometries with short lines
cites work: Extensions of GQ(4, 2): the totally regular case
cites work: On amply regular locally \(GQ(4,4)\)-graphs
cites work: Extended generalized quadrangles
full work available at URL: s106456241203012x
OpenAlex ID: W1973905832
description: scientific article; zbMATH DE number 6106457