# Vanishing Euler Characteristic of Circulants

In the article G. Rinaldo, F. Romeo, On the reduced Euler characteristic of the independence complex of Circulant graphs, the authors presented counterexamples to Hoshino's conjecture about the vanishing of the the reduced Euler characteristic of the independence complex of Circulant graphs. In this link it is possible to download a Magma algorithm to compute Circulants whose reduced Euler characteristic of the independence complex vanishes.

The command to run our implementation in the shell is the following:

magma VanishingEulerCharacteristic.txt

It produces an output file "Out.txt" that contains a unique circulant graph, the one in the picture that is made by Mathematica.