Geodesic
Identifying graph automorphisms using determining sets
The electronic journal of combinatorics, Tome 13 (2006)

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Zbl EuDML
A set of vertices $S$ is a determining set for a graph $G$ if every automorphism of $G$ is uniquely determined by its action on $S$. The determining number of a graph is the size of a smallest determining set. This paper describes ways of finding and verifying determining sets, gives natural lower bounds on the determining number, and shows how to use orbits to investigate determining sets. Further, determining sets of Kneser graphs are extensively studied, sharp bounds for their determining numbers are provided, and all Kneser graphs with determining number $2$, $3,$ or $4$ are given.
DOI : 10.37236/1104
Classification : 05C25
Mots-clés : Kneser graphs, determining number 
Debra L. Boutin. Identifying graph automorphisms using determining sets. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1104
@article{10_37236_1104,
     author = {Debra L. Boutin},
     title = {Identifying graph automorphisms using determining sets},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1104},
     zbl = {1111.05043},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1104/}
}
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