We study nonregular graphs with three eigenvalues. We determine all the ones with least eigenvalue &2, and give new infinite families of examples. 1998 Academic Press ## 1. Introduction In this paper we look at the graphs that are generalizations of strongly regular graphs (cf. [3, 6, 16]) by drop
On rank three graphs with a large eigenvalue
β Scribed by Carl Bumiller
- Publisher
- Elsevier Science
- Year
- 1978
- Tongue
- English
- Weight
- 337 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
## Gardiner, A., Almost rank three graphs, Discrete Mathematics 103 (1992) 253-257.
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
A graph is called of type k if it is connected, regular, and has k distinct eigenvalues. For example graphs of type 2 are the complete graphs, while those of type 3 are the strongly regular graphs. We prove that for any positive integer n, every graph can be embedded in n cospectral, non-isomorphic
Nilli, A., On the second eigenvalue of a graph, Discrete Mathematics 91 (1991) 207-210. It is shown that the second largest eigenvalue of the adjacency matrix of any G containing two edges the distance between which is at least 2k + 2 is at least (2G -l)/(k + 1).