# CSM

## Seminar

### Integer symmetric matrices with spectral radius at most 2.019

Seminar Room 1, Newton Institute

#### Abstract

All graphs with spectral radius (of their adjacency matrix) at most sqrt(2+sqrt(5)) = 2.05817... are known. In joint work with James McKee, we try to extend this result to general symmetric matrices with integer entries. As is clear from the title, we do not get quite as far. Apart from some trivial examples, all the matrices described by the title are represented by 'charged signed graphs' having adjacency matrices with entries 0,1 or -1.

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