Eigenvalues and extremal degrees of graphs
β Scribed by Vladimir Nikiforov
- Book ID
- 104036759
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 89 KB
- Volume
- 419
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
Let G be a graph whose Laplacian eigenvalues are 0 = Ξ» 1 Ξ» 2 β’ β’ β’ Ξ» n . We investigate the gap (expressed either as a difference or as a ratio) between the extremal non-trivial Laplacian eigenvalues of a connected graph (that is Ξ» n and Ξ» 2 ). This gap is closely related to the average density of c
## Abstract We show that the vertex set of any graph __G__ with __p__β©Ύ2 vertices can be partitioned into nonβempty sets __V__~1~, __V__~2~, such that the maximum degree of the induced subgraph γ__V__~i~γ does not exceed where p^i^ = |__V__^i^|, for __i__=1, 2. Furthermore, the structure of the in