With the wide application of graph theory in circuit layout, signal flow chart and power system, more and more attention has been paid to the network topology analysis method of graph theory. In this paper, we construct a graph transformation which can reflect the monotonicity of coefficients and reduce the number of graphs. A sharp lower bound for incidence energy in the tricyclic graphs is given and all the extremal structures are characterized. The most interesting things that we find two different classes tricyclic graphs have the same signless Laplacian characteristic polynomials and one of the extremal graphs beyond all expectations.

中文翻译：

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三轮图的入射能边界及其极值结构

随着图论在电路布局，信号流程图和电力​​系统中的广泛应用，越来越关注图论的网络拓扑分析方法。在本文中，我们构建了一个可以反映系数单调性并减少图数量的图变换。给出了三环图中入射能量的尖锐下限，并表征了所有极值结构。我们发现最有趣的事情是，两个不同类的三环图具有相同的无符号拉普拉斯特征多项式，并且是超出所有期望的极值图之一。