On the metric dimension of incidence graph of Möbius planes

Abstract

We study the metric dimension and optimal split-resolving sets of the point-circle incidence graph of a Möbius plane. We prove that the metric dimension of a Möbius plane of order $q$ is around $2q$, and that an optimal split-resolving set has cardinality between approximately $5q$ and $2.5q\log q$. We also prove that a smallest blocking set of a Möbius plane of order $q$ has at most $2q(1+\log (q+1))$ points.

References in corpus (1)

• On the metric dimension of affine planes, biaffine planes and generalized quadrangles