Concerning two conjectures on the set of fixed points of a complete rotation of a Cayley digraph |
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Authors: | Nicolas Lichiardopol |
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Institution: | I3S-ESSI, BP 145, 06903, Sophia Antipolis, France |
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Abstract: | In 1996, J.C. Bermond, T. Kodate, S. Perennes and N. Marlin conjectured that the set Fσ of fixed points of some complete rotation σ of the toroidal mesh TM(p)k is not separating (that is Fσ does not disconnect TM(p)k). They also conjectured that the set Fω of fixed points of any complete rotation ω of any Cayley digraph is not separating. In this paper, we prove the first conjecture and disprove the second one. |
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Keywords: | Author Keywords: Cayley digraph Complete rotation Fixed points Separating set |
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