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The determining number of Kneser graphs

 

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Author: Cáceres González, José
Garijo Royo, Delia
González Herrera, Antonio
Márquez Pérez, Alberto
Puertas González, María Luz
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2013
Published in: . Discrete Mathematics & Theoretical Computer Science 15(1): 1-14 (2013)
Document type: Article
Abstract: 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.
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URI: http://hdl.handle.net/11441/38829

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