Metrical regularity in the incidence graph of a finite linear space
type: Item
instance of: scholarly article
title: Metrical regularity in the incidence graph of a finite linear space
zbMATH Open document ID: 0555.05017
DOI: 10.1016/0012-365X(84)90076-1
author: Anne Delandtsheer
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: A linear space is an incidence structure (\({\mathcal P},{\mathcal L},I)\), where the elements of \({\mathcal P}\) are called points and the elements of \({\mathcal L}\) lines, any two points being incident with exactly one line and any line being incident with at least two points. In this paper the author investigates finite linear spaces whose incidence graph \({\mathcal G}\) satisfies a condition of the following type: Given six integers i, j, k, l, m, n, there is an integer c such that for any triple (u,v,w)\(\circ F\) vertices of \({\mathcal G}\), where a is a point and \(d(u,v)=i\), \(d(v,w)=j\), \(d(w,u)=k\), there are exactly c vertices of \({\mathcal G}\) which are at distance l from u, m from v, and n from w.
reviewed by: Mario Gionfriddo
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 3884176
zbMATH Keywords: finite linear spaces
zbMATH Keywords: incidence graph
zbMATH Keywords: distance
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3884176