On the distribution of eigenvalues of graphs
โ Scribed by Alexander Kelmans; Xuerong Yong
- Book ID
- 108316311
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 415 KB
- Volume
- 199
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
For a simple, undirected graph q n , let k i q n be the ith largest eigenvalue of q n . This paper presents mainly the following: 1. For n P 4, if q n is incomplete, then 2. Seven sucient and necessary conditions such that k 2 q n ร1. 3. k 3 q n ร1 implies that k j q n ร1Y j 3Y 4Y F F F Y n ร 1.
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