Configurations graphs of neighbourhood geometries
M. Abreu, Martin Funk, D. Labbate, Vito Napolitano · Contributions to Discrete Mathematics · 2008
Configurations of type (κ 2 + 1)κ give rise to κ-regular simple graphs via configuration graphs.On the other hand, neighbourhood geometries of C4-free κ-regular simple graphs on κ 2 + 1 vertices turn out to be configurations of type (κ 2 + 1)κ.We investigate which configurations of type (κ 2 + 1)κ are equal or isomorphic to the neighbourhood geometry of their configuration graph and conversely.We classify all such graphs and configurations for κ = 3 and for κ = 4 when the graphs admit a centre of radius 2.