The reflexive edge strength of toroidal fullerene

Abstract

AbstractA 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 [Formula: see text] and a vertex function χv from the vertex set to the set [Formula: see text] where [Formula: see text] 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 [Formula: see text] the edge weight [Formula: see text] is defined as the summation of the edge label [Formula: see text] itself and its two vertex labels [Formula: see text] and [Formula: see text] The reflexive edge strength of the graph Ω symbolized by, [Formula: see text] 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.

Keywords

• Fullerene
• toroidal polyhex
• edge irregular reflexive labeling
• reflexive edge strength