Let be a graph of order with vertices labeled as . Let be the degree of the vertex , for . The difference adjacency matrix of is the square matrix of order whose entry is equal to if the vertices and of are adjacent or and zero otherwise. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices. In this paper, some properties of its characteristic polynomial are studied. We also investigate the difference energy of a graph. In addition, we establish some upper and lower bounds for this new energy of graph.

中文翻译：

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图中拓扑指数之间存在差异的光谱特性

令其为顶点标记为的阶数图。让是顶点的程度，对。的差邻接矩阵是阶方阵，其 项等于 如果顶点和的是相邻的或否则为零。由于此索引与图的顶点度有关，因此我们的主要工具将是一个合适的矩阵，即对包含顶点度的经典邻接矩阵的修改。本文研究了其特征多项式的一些性质。我们还研究了图的差能量。另外，我们为图的这种新能量建立了一些上下限。