Representing and recognizing torus bundles over S1

As it is well-known, torus bundles over S-1 are identified by means of regular integer matrices of order two (see [S]). In the present paper an algorithmic procedure is described which allows to construct, directly from any matrix A is an element of GL(2; Z), an edge-coloured graph representing the torus bundle TB(A) associated to A. As a consequence, five topologically undetected elements of Lins's catalogue of orientable 3-manifolds (see [L]) are finally recognized as torus bundles over S-1.