A proof of a conjecture of Sabidussi on graphs idempotent under the lexicographic product |
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Authors: | P Ille |
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Institution: | Institut de Mathématiques de Luminy, CNRS-UMR 6206, 163 avenue de Luminy, Case 907, 13288 Marseille Cedex 09, France |
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Abstract: | In 1960, Sabidussi conjectured that if a graph G is isomorphic to the lexicographic product GG], then the wreath product of by itself is a proper subgroup of . A positive answer is provided by constructing an automorphism Ψ of GG] which satisfies: for every vertex x of G, there is an infinite subset I(x) of V(G) such that Ψ({x}×V(G))=I(x)×V(G). |
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Keywords: | Lexicographic product Idempotent Wreath product |
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