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<p>The number of spanning trees of a graph is an important characteristic of its reliability as a data transmission network. We found the maximal number of spanning trees in a cactus with a given number of vertices and also in a bipartite cactus with a given number of vertices. In particular, friendship graphs and Koch networks are extremal graphs.</p>

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ON THE MAXIMAL NUMBER OF SPANNING TREES IN CACTI WITH GIVEN ORDER

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • V. A. Voblyi,
  • D. A. Kononenko

摘要

The number of spanning trees of a graph is an important characteristic of its reliability as a data transmission network. We found the maximal number of spanning trees in a cactus with a given number of vertices and also in a bipartite cactus with a given number of vertices. In particular, friendship graphs and Koch networks are extremal graphs.