The Estrada index of trees
β Scribed by Zhibin Du; Bo Zhou
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 213 KB
- Volume
- 435
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let G be a simple graph of order n with m edges. Let the adjacency spectrum be {Ξ» 1 , Ξ» 2 , . . . In [J.A. PeΓ±a, I. Gutman, J. Rada, Estimating the Estrada index, Linear Algebra Appl. 427 (2007) 70-76], PeΓ±a et al. posed a conjecture that the star S n has maximum Estrada index for any tree of order
4, 6)-fullerene a b s t r a c t Suppose G is a graph and Ξ» 1 , Ξ» 2 , . . . Ξ» n are the eigenvalues of G. The Estrada index EE(G) of G is defined as the sum of the terms e Ξ» i , 1 β€ i β€ n. In this work some upper and lower bounds for the Estrada index of (4, 6)-fullerene graphs are presented.
## Abstract The generalized RandiΔ; index ${R}\_{-\alpha}(T)$ of a tree __T__ is the sum over the edges ${u}{v}$ of __T__ of $(d(u)d(v))^{-\alpha}$ where ${d}(x)$ is the degree of the vertex __x__ in __T__. For all $\alpha > 0$, we find the minimal constant $\beta\_{0}=\beta\_{0}(\alpha)$ such that