Bailey, Robert F.; Cáceres, José; Garijo, Delia; González, Antonio; Márquez, Alberto; Meagher, Karen; Puertas, María Luz Resolving sets for Johnson and Kneser graphs. (English) Zbl 1259.05051 Eur. J. Comb. 34, No. 4, 736-751 (2013). Summary: A set of vertices \(S\) in a graph \(G\) is a resolving set for \(G\) if, for any two vertices \(u,v\), there exists \(x\in S\) such that the distances \(d(u,x)\neq d(v,x)\). In this paper, we consider the Johnson graphs \(J(n,k)\) and Kneser graphs \(K(n,k)\), 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. Cited in 19 Documents MSC: 05C12 Distance in graphs 05C99 Graph theory Keywords:partial geometries; Hadamard matrices; Steiner systems; toroidal grids; Johnson graphs Software:GAP PDFBibTeX XMLCite \textit{R. F. Bailey} et al., Eur. J. Comb. 34, No. 4, 736--751 (2013; Zbl 1259.05051) Full Text: DOI arXiv