Scholarlink

<p>The cyclicity index of a&#xa0;strongly connected directed graph is the greatest common divisor of all its directed cycles and the cyclicity index of an arbitrary directed graph is the least common multiple of the cyclicity indices of all its maximal strongly connected subgraphs. The cyclicity index of a&#xa0;matrix is equal to cyclicity index of its critical subgraph, namely, subgraph of adjacent graph, consisting of all cycles with the maximal average weight. In this paper, we consider surjective linear transformations of non-negative and integer non-negative matrices preserving cyclicity index. We obtain the complete characterization of such maps and prove that they are automatically injective.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

ON LINEAR TRANSFORMATIONS PRESERVING CYCLICITY INDEX OF NONNEGATIVE MATRICES

  • 期刊论文

  • 发表日期：

    2026年1月1日

查看全文
  • A. V. Vlasov,
  • A. E. Guterman,
  • E. M. Kreines

摘要

The cyclicity index of a strongly connected directed graph is the greatest common divisor of all its directed cycles and the cyclicity index of an arbitrary directed graph is the least common multiple of the cyclicity indices of all its maximal strongly connected subgraphs. The cyclicity index of a matrix is equal to cyclicity index of its critical subgraph, namely, subgraph of adjacent graph, consisting of all cycles with the maximal average weight. In this paper, we consider surjective linear transformations of non-negative and integer non-negative matrices preserving cyclicity index. We obtain the complete characterization of such maps and prove that they are automatically injective.