##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Sebastian Cioaba

#### UCSD

## The spectral radius and the diameter of connected graphs

##### Abstract:

Recently, Wang, Chakrabarti, Wang and Faloutsos have shown that the spectral radius of a graph plays an important role in modeling virus propagation in networks. This led Van Dam and Kooij to consider the following problem: which connected graph on n nodes and diameter D has minimal spectral radius ? Van Dam and Kooij answered this question for $D=n-1,n-2,n-3,n/2,2,1$ and provided a conjecture for the case $D=n-e$, when e is fixed. In this talk, I give an overview of their work and I will outline a proof of their conjecture for $e=4$ and possible extensions for $e>4$. This is joint work in progress with Edwin Van Dam (University of Tilburg, The Netherlands).

### April 17, 2007

### 4:00 PM

### AP&M 7321

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