学术报告-Sanming Zhou (The University of Melbourne—墨尔本大学)-Perfect codes in Cayley graphs

2018年01月10日 13:49  


目:Perfect codes in Cayley graphs

报告人:Sanming Zhou (The University of Melbourne—墨尔本大学)

邀请人:刘晓刚

间:2018年1月25日(周四)上午10:00—11:30

点:友谊校区诚字楼201

要:A perfect t-code in a graph G = (V, E) is a subset C of V such that the t-neighbourhoods of the vertices in C form a partition of V, where t is a positive integer and the t-neighbourhood of a vertex is the set of vertices within distance t from it. Perfect t-codes in Hamming graph H(n, q) are precisely q-ary perfect t-codes of length n in the classical setting. A perfect 1-code in a graph is also called an efficient dominating set or independent perfect dominating set of the graph.

Perfect codes in Cayley graphs are a generalization of perfect codes under the Hamming or Lee metric, and perfect 1-codes in Cayley graphs are closely related to tilings of the underlying groups. In this talk I will give a short survey of perfect codes in Cayley graphs, with an emphasis on perfect 1-codes.

报告人简介:周三明,澳大利亚墨尔本大学数学与统计学院教授,澳大利亚组合数学学会主席,墨尔本-北京数学与统计虚拟研究中心主任;先后获国际组合数学及其应用学会Kirkman奖和澳大利亚研究委员会“未来研究员”称号;主要从事图论与组合数学的研究,已发表学术论文100余篇,是国际上知名的组合数学家。

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