The number of spanning trees in a network determines the totality of acyclic and connected components present within. This number is termed as complexity of the network. In this article, we address the closed formulae of the complexity of networks’ operations such as duplication (split, shadow, and vortex networks of ), sum (, , and ), product ( and ), semitotal networks ( and ), and edge subdivision of the wheel. All our findings in this article have been obtained by applying the methods from linear algebra, matrix theory, and Chebyshev polynomials. Our results shall also be summarized with the help of individual plots and relative comparison at the end of this article.

中文翻译：

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网络上一些广义操作的复杂性

网络中生成树的数量决定了其中存在的非循环和连接组件的总数。这个数字被称为网络的复杂性。在本文中，我们解决了网络操作复杂性的封闭公式，例如重复（分裂、阴影和涡旋网络）、总和（, ，和),产品 (和)、半全网络（和）和轮的边细分。我们在本文中的所有发现都是通过应用线性代数、矩阵理论和切比雪夫多项式的方法获得的。我们的结果也将在本文末尾的个别图和相对比较的帮助下进行总结。