Abstract
In this paper we deal with the problem of labeling the vertices, edges, and faces of a toroidal fullerene H-m(n) with mm hexagons by the consecutive integers from 1 up to vertical bar V(H-m(n))vertical bar + vertical bar E(H-m(n))vertical bar + F(H-m(n))vertical bar in such a way that the set of face-weights of 6-sided faces forms an arithmetic progression with common difference d, where by face-weight we mean the sum of the label of that face and the labels of vertices and edges surrounding that face.