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).
A surprising property of the least eigenvalue of a graph
β Scribed by Michael Doob
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 418 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
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## Abstract It is well known that the smallest eigenvalue of the adjacency matrix of a connected __d__βregular graph is at least β __d__ and is strictly greater than β __d__ if the graph is not bipartite. More generally, for any connected graph __G = (V, E)__, consider the matrix __Q = D + A__ wher
If the lines of the complete graph K,, are calmed so that no point is on more than +(n -1) lines of the same color or so that each point lies on more than $(5n + 8) lines of different colors, then K,, contains a cycle of length n with adjacent lines having different colors. Let the lines of a graph