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Graphs with Exactly Two Negative Eigenvalues

✍ Scribed by Aleksandar Torgašev

Publisher
John Wiley and Sons
Year
1985
Tongue
English
Weight
290 KB
Volume
122
Category
Article
ISSN
0025-584X

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✦ Synopsis

In this paper we determine all finite connected graphs whose spectiviri contains exactly two negative eigenvalues. The main theorem says that a graph hm exactly two negative eigenvalues if and only if its "canonical graph" (defined below) is one of nine particular graphs on 3, 4, 5 and G vertices.

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✍ Aleksander Torgašev 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 374 KB

Let P(n) be the class of all connected graphs having exactly n ~> 1 negative eigenvalues (including their multiplicities). In this paper we prove that the class P(n) contains only finitely many so-called canonical graphs. The analogous statement for the class Q(n) of all connected graphs having exac

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Nonregular Graphs with Three Eigenvalues
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