José Cáceres ; Delia Garijo ; Antonio González ; Alberto Márquez ; Marıa Luz Puertas - The determining number of Kneser graphs

dmtcs:634 - Discrete Mathematics & Theoretical Computer Science, January 28, 2013, Vol. 15 no. 1 -
The determining number of Kneser graphsArticle

Authors: José Cáceres 1; Delia Garijo ORCID2; Antonio González ORCID2; Alberto Márquez 1,2; Marıa Luz Puertas

  • 1 Department of Statistics and Applied Mathematics [Almeria]
  • 2 Department of Applied Mathematics I [Sevilla]

A set of vertices S is a determining set of a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of G is the minimum cardinality of a determining set of G. This paper studies the determining number of Kneser graphs. First, we compute the determining number of a wide range of Kneser graphs, concretely Kn:k with n≥k(k+1) / 2+1. In the language of group theory, these computations provide exact values for the base size of the symmetric group Sn acting on the k-subsets of 1,..., n. Then, we establish for which Kneser graphs Kn:k the determining number is equal to n-k, answering a question posed by Boutin. Finally, we find all Kneser graphs with fixed determining number 5, extending the study developed by Boutin for determining number 2, 3 or 4.

Volume: Vol. 15 no. 1
Section: Graph Theory
Published on: January 28, 2013
Accepted on: June 9, 2015
Submitted on: December 21, 2011
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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