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Graphs with a Small Number of Nonnegative Eigenvalues

✍ Scribed by Miroslav Petrović

Publisher
Springer Japan
Year
1999
Tongue
English
Weight
130 KB
Volume
15
Category
Article
ISSN
0911-0119

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📜 SIMILAR VOLUMES

On graphs with a fixed number of negativ
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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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If D is an acyclic digraph, its competition graph is an undirected graph with the same vertex set and an edge between vertices x and y if there is a vertex a so that (x, a) and (y, a) are both arcs of D. If G is any graph, G together with sufficiently many isolated vertices is a competition graph, a

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Let G be a graph on n vertices. We show that if the total number of isomorphism types of induced subgraphs of G is at most &II', where E < lo-\*', then either G or its complement contain an independent set on at least (1 -4e)n vertices. This settles a problem of Erdiis and Hajnal.