论文标题
查找奇特的镜面图
Finding singularly cospectral graphs
论文作者
论文摘要
两个具有相同频谱的图是共同的。一对奇异的镜面图由两个图形形成，使其非零特征值的绝对值重合。显然，一对骑术图也很奇特，但相反可能不是正确的。如果它们的非零特征值及其倍数一致，则两个图几乎是镜面的。在本文中，我们提出了一对图表的必要条件，使其具有奇异的清晰度，并回答了Nikiforov发布的问题。此外，我们构建了一对无限既定的奇异图，具有无限数量的顶点。很明显，几乎既定的图形也是奇异的，但相反的不一定是正确的，我们提出了这两个概念的图形家庭：几乎是共同的和奇异的合适性。
Two graphs having the same spectrum are said to be cospectral. A pair of singularly cospectral graphs is formed by two graphs such that the absolute values of their nonzero eigenvalues coincide. Clearly, a pair of cospectral graphs is also singularly cospectral but the converse may not be true. Two graphs are almost cospectral if their nonzero eigenvalues and their multiplicities coincide. In this paper, we present necessary and sufficient conditions for a pair of graphs to be singularly cospectral, giving an answer to a problem posted by Nikiforov. In addition, we construct an infinite family of pairs of noncospectral singularly cospectral graphs with unbounded number of vertices. It is clear that almost cospectral graphs are also singularly cospectral but the converse is not necessarily true, we present families of graphs where both concepts: almost cospectrality and singularly cospectrality agree.
