On the roots of strongly connected reliability polynomials
β Scribed by J. I. Brown; K. Dilcher
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 199 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0028-3045
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π SIMILAR VOLUMES
It is proved that the chromatic polynomial of a connected graph with n vertices and m edges has a root with modulus at least (m&1)Γ(n&2); this bound is best possible for trees and 2-trees (only). It is also proved that the chromatic polynomial of a graph with few triangles that is not a forest has a
## Abstract We examine some properties of the 2βvariable greedoid polynomial __f__(__GΒ·,t,z__) when __G__ is the branching greedoid associated to a rooted graph or a rooted directed graph. For rooted digraphs, we show a factoring property of __f__(__GΒ·,t,z__) determines whether or not the rooted di
We give bounds for the roots of such polynomials with complex coefficients. These bounds are much smaller than for general polynomials.