Abstract
A toroidal fullerene (toroidal polyhex) is a cubic bipartite graph embedded on the torus such that each face is a hexagon. The total k-labeling is defined as a combination of an edge function chi(e) from the edge set to the set {1,2, horizontal ellipsis ,k(e)} and a vertex function chi(v) from the vertex set to the set {0,2, horizontal ellipsis ,2k(v)}, where k=max{k(e),2k(v)}. The total k-labeling of graph omega such that every two distinctive edges have distinctive weight is called an edge irregular reflexive k-labeling, where for any edge x(1)x(2), the edge weight wt(x(1)x(2)) is defined as the summation of the edge label chi e(x1x2) itself and its two vertex labels chi(v)(x(1)) and chi(v)(x2). The reflexive edge strength of the graph omega symbolized by, res(omega) is the smallest k for which the graph omega has an edge irregular reflexive k-labeling. In this paper we determine the exact value of reflexive edge strength of toroidal polyhexes.