Resolving sets for Johnson and Kneser graphs

  • Authors:

  • Robert F. Bailey;José CáCeres;Delia Garijo;Antonio GonzáLez;Alberto MáRquez;Karen Meagher;MaríA Luz Puertas

  • Affiliations:

  • Department of Mathematics, Ryerson University, 350 Victoria St., Toronto, Ontario M5B 2K3, Canada;Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Ctra.Sacramento s/n, Almería 04120, Spain;Departamento de Matemática Aplicada I, Universidad de Sevilla, Av.Reina Mercedes s/n, Sevilla 41012, Spain;Departamento de Matemática Aplicada I, Universidad de Sevilla, Av.Reina Mercedes s/n, Sevilla 41012, Spain;Departamento de Matemática Aplicada I, Universidad de Sevilla, Av.Reina Mercedes s/n, Sevilla 41012, Spain;Department of Mathematics and Statistics, University of Regina, 3737 Wascana Parkway, Regina, Saskatchewan S4S 0A2, Canada;Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Ctra.Sacramento s/n, Almería 04120, Spain

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2013

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Abstract

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@?S such that the distances d(u,x)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.