论文标题
最多有两个非零的绝对特征值的图形
Graphs with at most two nonzero distinct absolute eigenvalues
论文作者
论文摘要
Nikiforov在他的调查“超越图形能量：图形和矩阵的规范”（2016年）中提出了两个有关图表的问题，这些问题分别在下界和图形能量的上限分别在图中获得平等。我们表明，这些图最多具有两个非零的绝对特征值，并根据它们可以拥有的频谱类型来研究提出的问题。在大多数情况下，所有图都表征了。另外给出了无限的图。我们还表明，所有符合问题中所需属性的图形都是积分的，除了完整的两分图$ k_ {p，q} $和带有连接的组件$ k_ {p，q} $的断开图形，其中$ pq $不是一个完美的正方形。
In his survey "Beyond graph energy: Norms of graphs and matrices" (2016), Nikiforov proposed two problems concerning characterizing the graphs that attain equality in a lower bound and in a upper bound for the energy of a graph, respectively. We show that these graphs have at most two nonzero distinct absolute eigenvalues and investigate the proposed problems organizing our study according to the type of spectrum they can have. In most cases all graphs are characterized. Infinite families of graphs are given otherwise. We also show that all graphs satifying the properties required in the problems are integral, except for complete bipartite graphs $K_{p,q}$ and disconnected graphs with a connected component $K_{p,q}$, where $pq$ is not a perfect square.
