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The Estrada index of trees

✍ Scribed by Zhibin Du; Bo Zhou


Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
213 KB
Volume
435
Category
Article
ISSN
0024-3795

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On Estrada index of trees
✍ Jianbin Zhang; Bo Zhou; Jianping Li πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 230 KB
Estimating the Estrada index
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On the Estrada index conjecture
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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

Bounds on the Estrada index of ISR -full
✍ A.R. Ashrafi; G.H. Fath-Tabar πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 225 KB

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 ≀ i ≀ n. In this work some upper and lower bounds for the Estrada index of (4, 6)-fullerene graphs are presented.

The generalized Randić index of trees
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## Abstract The generalized Randić; 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