  In this paper we study the motion of two particles diffusing on
low-dimensional discrete structures in presence of a hard-core repulsive
interaction. We show that the problem can be mapped in two decoupled problems
of single particles diffusing on different graphs by a transformation we call
'diffusion graph transform'. This technique is applied to study two specific
cases: the narrow comb and the ladder lattice. We focus on the determination of
the long time probabilities for the contact between particles and their
reciprocal crossing. We also obtain the mean square dispersion of the particles
in the case of the narrow comb lattice. The case of a sticking potential and of
'vicious' particles are discussed.
