# More on Numbers and Graphs

@article{Knill2019MoreON, title={More on Numbers and Graphs}, author={Oliver Knill}, journal={ArXiv}, year={2019}, volume={abs/1905.13387} }

In this note we revisit a "ring of graphs" Q in which the set of finite simple graphs N extend the role of the natural numbers and the signed graphs Z extend the role of the integers. We point out the existence of a norm which allows to complete Q to a real or complex Banach algebra R or C.

## 4 Citations

### REMARKS ABOUT THE ARITHMETIC OF GRAPHS

- Mathematics
- 2021

The arithmetic of N ⊂ Z ⊂ Q ⊂ R can be extended to a graph arithmetic N ⊂ Z ⊂ Q ⊂ R, where N is the semi-ring of finite simple graphs and where Z,Q are integral domains culminating in a Banach…

### Extending the vision of Shannon

- Mathematics
- 2021

The arithmetic of N ⊂ Z ⊂ Q ⊂ R can be extended to a graph arithmetic N ⊂ Z ⊂ Q ⊂ R, where N is the semi-ring of finite simple graphs and where Z,Q are integral domains culminating in a Banach…

### Remarks about the Arithmetic of Graphs

- MathematicsArXiv
- 2021

This work illustrates the compatibility with topology and spectral theory of multiplicative linear functionals like Euler characteristic, the Poincaré polynomial, zeta functions, which can be extended naturally naturally to graph arithmetic.

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