We give new bounds on eigenvalue of graphs which imply some known bounds. In particular, if T(G) is the maximum sum of degrees of vertices a~t to a vertex in a graph G, the largest eigenvalue p(G) of G satisfies p(G) <~ ~IT(G) with equality if and only if either G is regular or G is bipartite and su
Bounds on eigenvalues and chromatic numbers
β Scribed by Cao, D
- Book ID
- 120116007
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 361 KB
- Volume
- 270
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
## Abstract In this paper we discuss some estimates for upper bounds on a number of chromatic parameters of a multigraph. In particular, we show that the total chromatic number for an __n__βorder multigraph exceeds the chromatic index by the smallest __t__ such that __t__! > __n__.
## Abstract Bounds on the sum and product of the chromatic numbers of __n__ factors of a complete graph of order __p__ are shown to exist. The wellβknown theorem of Nordhaus and Gaddum solves the problem for __n__ = 2. Strict lower and some upper bounds for any __n__ and strict upper bounds for __n