Artículo
The determining number of Kneser graphs
Autor/es | Cáceres González, José
Garijo Royo, Delia González Herrera, Antonio Márquez Pérez, Alberto Puertas González, María Luz |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2013 |
Fecha de depósito | 2016-03-18 |
Publicado en |
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Resumen | 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 ... 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. |
Ficheros | Tamaño | Formato | Ver | Descripción |
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The deterrmining number.pdf | 394.3Kb | [PDF] | Ver/ | |