ORDERS IN QUATERNION ALGEBRA AND RAMANUJAN GRAPHS

Insuk Kim (Korea)

Received September 12, 2007

Abstract

Brandt matrices associated with the primitive orders in quaternion algebra are representations of Hecke operators. These Brandt matrices give the adjacency matrices of a Ramanujan graph allowing multiple edges and loops.

Keywords and phrases: Ramanujan graph, magnifier, girth, loop, Brandt matrix, Hecke operators, adjacency matrix.