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Resolving sets for Johnson and Kneser graphs

 

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Opened Access Resolving sets for Johnson and Kneser graphs
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Author: Bailey, Robert F.
Cáceres González, José
Garijo Royo, Delia
González Herrera, Antonio
Márquez Pérez, Alberto
Meagher, Karen
Puertas González, María Luz
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2013
Published in: European Journal of Combinatorics, 34 (4), 736-751.
Document type: Article
Abstract: A set of vertices SS in a graph GG is a resolving set for GG if, for any two vertices u,vu,v, there exists x∈Sx∈S such that the distances d(u,x)≠d(v,x)d(u,x)≠d(v,x). In this paper, we consider the Johnson graphs J(n,k)J(n,k) and Kneser graphs K(n,k)K(n,k), and obtain various constructions of resolving sets for these graphs. As well as general constructions, we show that various interesting combinatorial objects can be used to obtain resolving sets in these graphs, including (for Johnson graphs) projective planes and symmetric designs, as well as (for Kneser graphs) partial geometries, Hadamard matrices, Steiner systems and toroidal grids.
Size: 263.4Kb
Format: PDF

URI: http://hdl.handle.net/11441/38816

DOI: http://dx.doi.org/10.1016/j.ejc.2012.10.008

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