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EnglishCongurations of type $(\kappa^2 +1)_{\kappa}$ give rise to $\kappa$--regular simple graphs via conguration graphs. On the other hand, neighbourhood geometries of $C_4$--free $\kappa$--regular simple graphs on $\kappa^2 +1$ vertices turn out to be congurations of type $(\kappa^2 +1)_{\kappa}$. We investigate which congurations of type $(\kappa^2 +1)_{\kappa}$ are equal or isomorphic to the neighbourhood geometry of their conguration graph and conversely. We classify all such graphs and congurations for $\kappa = 3$ and for $\kappa = 4$ when the graphs admit a centre of radius 2.
http://hdl.handle.net/11563/9231| Titolo: | Configuration Graphs of Neighbourhood Geometries |
| Autori interni: | ABREU, Marien FUNK, Martin LABBATE, Domenico |
| Data di pubblicazione: | 2008 |
| Rivista: | CONTRIBUTIONS TO DISCRETE MATHEMATICS |
| Abstract: | Congurations of type $(\kappa^2 +1)_{\kappa}$ give rise to $\kappa$--regular simple graphs via conguration graphs. On the other hand, neighbourhood geometries of $C_4$--free $\kappa$--regular simple graphs on $\kappa^2 +1$ vertices turn out to be congurations of type $(\kappa^2 +1)_{\kappa}$. We investigate which congurations of type $(\kappa^2 +1)_{\kappa}$ are equal or isomorphic to the neighbourhood geometry of their conguration graph and conversely. We classify all such graphs and congurations for $\kappa = 3$ and for $\kappa = 4$ when the graphs admit a centre of radius 2. |
| Handle: | http://hdl.handle.net/11563/9231 |
| Appare nelle tipologie: | 1.1 Articolo su Rivista |
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