保持循环指数的热带矩阵的非满射线性变换

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, CYBERNETICS

Kybernetika Pub Date : 2023-01-19 DOI:10.14736/kyb-2022-5-0691

Alexander Guterman, Elena Kreines, Alexander Vlasov

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引用次数: 2

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Non-surjective linear transformations of tropical matrices preserving the cyclicity index

The cyclicity index of a matrix is the cyclicity index of its critical subgraph, namely, the sub-graph of the adjacency graph which consists of all cycles of the maximal average weight. The cyclicity index of a graph is the least common multiple of the cyclicity indices of all its maximal strongly connected subgraphs, and the cyclicity index of a strongly connected graph is the least common divisor of the lengths of its (directed) cycles. In this paper we obtain the characterization of linear, possibly non-surjective, transformations of tropical matrices preserving the cyclicity index. It appears that non-bijective maps with these properties exist and all maps are exhausted by transposition, renumbering of vertices, Hadamard multiplication with a matrix of a certain special structure, and certain diagonal transformation. Moreover, only diagonal transformation can be non-bijective.

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来源期刊

Kybernetika 工程技术-计算机：控制论

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： Kybernetika is the bi-monthly international journal dedicated for rapid publication of high-quality, peer-reviewed research articles in fields covered by its title. The journal is published by Nakladatelství Academia, Centre of Administration and Operations of the Czech Academy of Sciences for the Institute of Information Theory and Automation of The Czech Academy of Sciences. Kybernetika traditionally publishes research results in the fields of Control Sciences, Information Sciences, Statistical Decision Making, Applied Probability Theory, Random Processes, Operations Research, Fuzziness and Uncertainty Theories, as well as in the topics closely related to the above fields.