The distance energy of a graph is defined as the sum of absolute values of distance eigenvalues of the graph. The distance energy of a graph plays an important role in many fields. By constructing a new polynomial, we transform a problem on the sum of the absolute values of the roots of a quadratic polynomial into a problem on the largest root of a cubic polynomial. Hence, we give a new and shorter proof on the change of distance energy of a complete bipartite graph due to edge deletion, which was given by Varghese et al.

中文翻译：

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关于完全二部图的距离能量由于边缘删除而发生的变化

图的距离能量定义为图的距离特征值的绝对值之和。图的距离能量在许多领域中都起着重要作用。通过构造一个新的多项式，我们将二次多项式根的绝对值之和上的问题转换为三次多项式最大根上的问题。因此，我们对由于边缘缺失而导致的完整二部图的距离能量的变化给出了新的和较短的证明，这由Varghese等人给出。