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The localization number of designs
Author(s) -
Bonato Anthony,
Huggan Melissa A.,
Marbach Trent G.
Publication year - 2021
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21762
Subject(s) - mathematics , combinatorics , affine transformation , block design , graph , projective plane , discrete mathematics , incidence (geometry) , pure mathematics , geometry , correlation
We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via distance probes. The localization number of a graph G , written ζ ( G ) , is the minimum number of cops needed to ensure the robber's capture. We present bounds on the localization number of incidence graphs of balanced incomplete block designs. Exact values of the localization number are given for the incidence graphs of projective and affine planes. Bounds are given for Steiner systems and for transversal designs.