Signed analogue of line graphs and their smallest eigenvalues
Signed analogue of line graphs and their smallest eigenvalues
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DOI：
10.1002/jgt.22699
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发表时间：
2020-03
影响因子：
0.9
通讯作者：
Alexander L. Gavrilyuk;A. Munemasa;Y. Sano;T. Taniguchi
中科院分区：
文献类型：
--
作者：
Alexander L. Gavrilyuk;A. Munemasa;Y. Sano;T. Taniguchi
在本文中，我们证明了最小特征值严格大于 − 2 且最小度足够大的每个连通有符号图都相当于完整图的切换。这是霍夫曼定理的带符号模拟。证明基于我们为埃尔米特矩阵制定的霍夫曼极限定理，以及霍夫曼图和线图概念的扩展以设置符号图。
In this article, we show that every connected signed graph with smallest eigenvalue strictly greater than − 2 and large enough minimum degree is switching equivalent to a complete graph. This is a signed analogue of a theorem of Hoffman. The proof is based on what we call Hoffman's limit theorem which we formulate for Hermitian matrices, and also the extension of the concept of Hoffman graph and line graph for the setting of signed graphs.