Metrical regularity in the incidence graph of a finite linear space
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.
scientific article; zbMATH DE number 3884176