On graphs with the smallest eigenvalue at least -1 - √2, part I
On graphs with the smallest eigenvalue at least -1 - √2, part I
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在具有最小特征值至少 -1 - √2 的图上，第一部分
DOI：
10.26493/1855-3974.35.fe9
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
T. Taniguchi
中科院分区：
文献类型：
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作者：
T. Taniguchi
关于最小特征值至少为-2的图有很多结果。作为下一步，A。J.霍夫曼提出研究最小特征值至少为-1-12的图。为了处理这类图，R. Woo和A. Neumaier引入了霍夫曼图的概念，并定义了依赖于一族霍夫曼图的线图的一个新的推广。他们证明了一个定理类似于霍夫曼的，使用一个特殊的家庭组成的四个同构类。在本文中，我们处理一个推广的基础上家庭H小于他们处理的，但包括广义线图的意义上的霍夫曼。主要结果是顶点数至少为8的H线图的覆盖是唯一的。
There are many results on graphs with the smallest eigenvalue at least−2. As a next step, A. J. Hoffman proposed to study graphs with the smallest eigenvalue at least −1 − √ 2. In order to deal with such graphs, R. Woo and A. Neumaier introduced the concept of a Hoffman graph, and defined a new generalization of line graphs which depends on a family of Hoffman graphs. They proved a theorem analogous to Hoffman’s, using a particular family consisting of four isomorphism classes. In this paper, we deal with a generalization based on a family H smaller than the one which they dealt with, yet including generalized line graphs in the sense of Hoffman. The main result is that the cover of an H -line graph with at least 8 vertices is unique.