The reflexive edge strength of toroidal fullerene

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 χe from the edge set to the set and a vertex function χv from the vertex set to the set where The total k-labeling of graph Ω such that every two distinctive edges have distinctive weight is called an edge irregular reflexive k-labeling, where for any edge the edge weight is defined as the summation of the edge label itself and its two vertex labels and The reflexive edge strength of the graph Ω symbolized by, is the smallest k for which the graph Ω has an edge irregular reflexive k-labeling. In this paper we determine the exact value of reflexive edge strength of toroidal polyhexes.