Abstract

The present work deals with the characteristic polynomial of Laplacian matrix for circulant graphs. We show that it can be decomposed into a finite product of algebraic function evaluated at the roots of a linear combination of Chebyshev polynomials. As an important consequence of this result, we get the periodicity of characteristic polynomials evaluated at the prescribed integer values. Moreover, we can show that the characteristic polynomials of circulant graphs are always perfect squares up to explicitly given linear factors.

中文翻译：

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循环图拉普拉斯特征多项式的结构研究

摘要

目前的工作涉及循环图拉普拉斯矩阵的特征多项式。我们证明它可以分解为在切比雪夫多项式线性组合的根处评估的代数函数的有限积。作为该结果的一个重要结果，我们得到了在规定整数值下评估的特征多项式的周期性。此外，我们可以证明循环图的特征多项式对于明确给定的线性因子始终是完美的平方。