Pseudoline arrangement graphs: degree sequences and eccentricities [article]

Sandip Das, Siddani Bhaskara Rao, Uma kant Sahoo
2021 arXiv   pre-print
A pseudoline arrangement graph is a planar graph induced by an embedding of a (simple) pseudoline arrangement. We study the corresponding graph realization problem and properties of pseudoline arrangement graphs. In the first part, we give a simple criterion based on the degree sequence that says whether a degree sequence will have a pseudoline arrangement graph as one of its realizations. In the second part, we study the eccentricities of vertices in such graphs. We observe that the diameter
more » ... aximum eccentricity of a vertex in the graph) of any pseudoline arrangement graph on n pseudolines is n-2. Then we characterize the diametrical vertices (whose eccentricity is equal to the graph diameter) of pseudoline arrangement graphs. These results hold for line arrangement graphs as well.
arXiv:2103.02283v1 fatcat:fmpde3vwsbfr3bzxfbwg252mfq