Transposition graph is defined as a Cayley graph over the symmetric group generated by all transpositions. It is known that all eigenvalues of are integers. Moreover, zero is its eigenvalue for any . But the exact distribution of the spectrum of the graph is unknown. In this paper we prove that integers from the interval lie in the spectrum of for any .

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转置图的不同特征值

转置图被定义为由所有转置生成的对称群上的凯莱图。已知 的所有特征值都是整数。此外，零是任何 的特征值。但该图频谱的确切分布尚不清楚。在本文中，我们证明区间中的整数位于任意 的谱中。