Super face d-antimagic labeling for disjoint union of toroidal fullerenes

Abstract

The discovery of the fullerene molecules and related forms of carbon such as nanotubes has generated an explosion of activity in chemistry, physics, and materials science. Classical fullerene is an all-carbon molecule in which the atoms are arranged on a pseudospherical framework made up entirely of pentagons and hexagons. A toroidal fullerene (toroidal polyhex) is a cubic bipartite graph embedded on the torus such that each face is a hexagon. In this paper we examine the existence of entire labeling, where face-weights of all 6-sided faces of disjoint union of toroidal fullerenes form an arithmetic progression with common difference d ∈ {1, 2, 3}.

Computing Zagreb Indices and Zagreb Polynomials of Fullerene, Butterfly and Benes Networks

“…The discovery of the fullerene molecules and related forms of carbon such as nanotubes has generated an explosion of activity in chemistry, physics, and materials science. A classical fullerene is an all-carbon molecule in which the atoms are arranged on a pseudospherical framework made up entirely of pentagons and hexagons, [27]. Its molecular graph is a finite trivalent graph embedded on the surface of a sphere with only hexagonal and (exactly 12) pentagonal faces.…”

New Results of Face Labeling for Some Plane Graphs

“…In [5], [6] the authors described super d-antimagic labelings of type (1, 1, 1) for generalized prism and disjoint union of generalized prisms. The super d-antimagic labeling of type (1, 1, 1) for toroidal fullerenes and disjoint union of toroidal fullerenes has been described in [7] and for Klein bottle fullerenes described in [8]. For subdivision of wheel graphs can be found in [9].…”

A New Graphical Representation of the Old Algebraic Structure

“…It is important to note that chemical graph theory has benefted much from mathematical chemistry [37][38][39]. Many of the invariants found in chemical graph theory, like indices or descriptors, are used in a variety of commercial areas, most notably in the chemical and pharmaceutical industries [40,41].…”