A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v. The metric dimensionμ(Γ) is the smallest size of a resolving set for Γ. We consider the metric dimension of the dual polar graphs, and show that it is at most the rank over R of the incidence matrix of the corresponding polar space. We then compute this rank to give an explicit upper bound on the metric dimension of dual polar graphs, as well as the halved dual polar graphs.

Bailey, R., Spiga, P. (2023). Metric dimension of dual polar graphs. ARCHIV DER MATHEMATIK, 120(5), 467-478 [10.1007/s00013-023-01829-2].

Metric dimension of dual polar graphs

Spiga P.
2023

Abstract

A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v. The metric dimensionμ(Γ) is the smallest size of a resolving set for Γ. We consider the metric dimension of the dual polar graphs, and show that it is at most the rank over R of the incidence matrix of the corresponding polar space. We then compute this rank to give an explicit upper bound on the metric dimension of dual polar graphs, as well as the halved dual polar graphs.
Articolo in rivista - Articolo scientifico
Dual polar graph; Metric dimension; Resolving set;
English
16-mar-2023
2023
120
5
467
478
open
Bailey, R., Spiga, P. (2023). Metric dimension of dual polar graphs. ARCHIV DER MATHEMATIK, 120(5), 467-478 [10.1007/s00013-023-01829-2].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/415959
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