Cayley Graph Automatic Groups Are Not Necessarily Cayley Graph Biautomatic

机译：Cayley图自动组不是必需的Cayley图Biautomatic

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摘要

We 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.

机译：我们表明，有不是非自动Cayley图的Cayley图自动组。此外，我们表明存在具有不确定共轭问题的Cayley图自动组，并且在Cayley图自动组的类别中同构问题是不确定的。

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来源
《Language and automata theory and applications.》|2012年|p.401-407|共7页
会议地点 A Coruna(ES);A Coruna(ES)
作者
Alexei Miasnikov; Zoran Sunic;
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作者单位

Department of Mathematical Sciences, Stevens Institute, Castle Point on Hudson Hoboken, NJ 07030-5991, USA;

Department of Mathematics, Texas AM University, MS-3368 College Station, TX 77843-3368, USA;

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会议组织
原文格式 PDF
正文语种 eng
中图分类程序语言、算法语言;程序语言、算法语言;
关键词
automatic structure; cayley graph automatic group; cayley graph biautomatic group; conjugacy problem; isomorphism problem;

机译：自动结构cayley图自动分组； cayley图双自动群；接合问题同构问题;

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1. CAYLEY GRAPHS ISOMORPHIC TO THE PRODUCT OF TWO CAYLEY GRAPHS [J] . Abdollahi Alireza, Loghman Amir Ars Combinatoria: An Australian-Canadian Journal of Combinatorics . 2016,第Null期

机译：Cayley图与两个Cayley图的产品同构
2. Vertex-transitive generalized Cayley graphs which are not Cayley graphs [J] . Hujdurovic Ademir, Kutnar Klavdija, Marusic Dragan European journal of combinatorics . 2015,第Null期

机译：非Cayley图的顶点传递广义Cayley图
3. ON NON-CAYLEY VERTEX-TRANSITIVE GRAPHS AND THE META-CAYLEY GRAPHS [J] . Eric Mwambene Quaestiones mathematicae . 2011,第4期

机译：关于非Cayley顶点传递图和Meta-Cayley图
4. Cayley DHTs — A Group-Theoretic Framework for Analyzing DHTs Based on Cayley Graphs [C] . Changtao Qu, Wolfgang Nejdl, Matthias Kriesell International Symposium on Parallel and Distributed Processing and Applications(ISPA 2004); 20041213-15; Hong Kong(CN) . 2004

机译：Cayley DHTs —基于Cayley图的DHT分组理论框架
5. Extremal Metric and Topological Properties of Vertex Transitive and Cayley Graphs [D] . Fraser, James. 2020

机译：顶点及传递和Cayley图的极值度量和拓扑特性
6. Cayley Bipolar Fuzzy Graphs [O] . Noura O. Alshehri, Muhammad Akram 2013

机译：Cayley双极模糊图
7. A note on vertex-transitive non-Cayley graphs from Cayley graphs generated by involutions [O] . Tomanová Jana 2010

机译：关于通过对合生成的Cayley图的顶点传递非Cayley图的注记
8. Random subgraphs of Cayley graphs over P-groups [R] . Reidys, C. M. 1997

机译：关于p-群的Cayley图的随机子图

Cayley Graph Automatic Groups Are Not Necessarily Cayley Graph Biautomatic

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