“…We continue the study of symmetric spaces of graphs which started in [1]. By a class of graphs is meant a set of ordinary graphs closed under the operation of renaming vertices.…”
Section: Introductionmentioning
confidence: 99%
“…In [1], classes of graphs closed under addition modulo 2 and deletion of isolated vertices were considered; it was proved that there were precisely five such classes. It is obvious that there exist infinitely many classes which are closed under addition modulo 2 only (for example, for any k the set of all graphs with at least k vertices is such a class).…”
We consider sets of graphs which are closed under the symmetric difference and renaming of vertices. We prove that for any n there are at most 14 such sets consisting of graphs with n vertices.
“…We continue the study of symmetric spaces of graphs which started in [1]. By a class of graphs is meant a set of ordinary graphs closed under the operation of renaming vertices.…”
Section: Introductionmentioning
confidence: 99%
“…In [1], classes of graphs closed under addition modulo 2 and deletion of isolated vertices were considered; it was proved that there were precisely five such classes. It is obvious that there exist infinitely many classes which are closed under addition modulo 2 only (for example, for any k the set of all graphs with at least k vertices is such a class).…”
We consider sets of graphs which are closed under the symmetric difference and renaming of vertices. We prove that for any n there are at most 14 such sets consisting of graphs with n vertices.
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