In the note, we present an upper bound for the spectral radius of Laplacian matrix of a graph in terms of a "2-degree" of a vertex.
On the Eigenvalues of a Graph
โ Scribed by H.B. Walikar; H.S. Ramane
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 145 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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).
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.