  We present a generalization of the construction of graphs by Lubotzky,
Phillips and Sarnak in their celebrated article "Ramanujan graphs". The new
approach consists in using octonion algebras rather than quaternions. A key
tool is the existing result of the unique factorization of integral octonions.
The families obtained by this mean present not only the same spectral property
that make them good expanders, but also show a larger girth, yielding a new
record for regular graphs.
