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Cayley Graph Automatic Groups Are Not Necessarily Cayley Graph Biautomatic
Lecture Notes in Computer Science, 2012We show that there are Cayley graph automatic groups that are not Cayley graph biautomatic. In addition, we show that there are Cayley graph automatic groups with undecidable Conjugacy Problem and that the Isomorphism Problem is undecidable in the class of Cayley graph automatic groups.
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When is the cayley graph of a semigroup isomorphic to the cayley graph of a group
Mathematica Slovaca, 2017Abstract It is well known that Cayley graphs of groups are automatically vertex-transitive. A pioneer result of Kelarev and Praeger implies that Cayley graphs of semigroups can be regarded as a source of possibly new vertex-transitive graphs.
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Discrete-time quantum walk on the Cayley graph of the dihedral group
Quantum Information Processing, 2018The finite dihedral group generated by one rotation and one flip is the simplest case of the non-Abelian group. Cayley graphs are diagrammatic counterparts of groups.
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