ABSTRACT

A graph G is called triangle-free if G does not contain a triangle as an induced subgraph. Let ${\mathcal{H}}_n$ be the set of triangle-free graphs of order n with six non-zero eigenvalues. In this paper, we find 19 graphs of ${\mathcal{H}}_n$, and we show that the other graphs of ${\mathcal{H}}_n$ can be constructed from these 19 graphs by adding some congruent vertices. Hence we completely characterize the triangle-free graphs with six non-zero eigenvalues.

中文翻译：

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具有六个非零特征值的无三角形图

摘要

如果G不包含作为诱导子图的三角形，则将图G称为无三角形。让${\mathcal{H}}_{ñ}$是具有六个非零特征值的n阶无三角形图的集合。在本文中，我们找到了19个图${\mathcal{H}}_{ñ}$，我们证明了 ${\mathcal{H}}_{ñ}$通过添加一些全等的顶点，可以从这19个图构建图。因此，我们完全表征了具有六个非零特征值的无三角形图。